Electromagnetic Radiation
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[{"Name":"Electromagnetic Radiation","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Electromagnetic Waves","Duration":"6m 37s","ChapterTopicVideoID":20095,"CourseChapterTopicPlaylistID":154565,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20095.jpeg","UploadDate":"2019-07-10T23:05:23.5470000","DurationForVideoObject":"PT6M37S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:05.549","Text":"In this video, we\u0027ll discuss a few points related to electromagnetic waves."},{"Start":"00:05.549 ","End":"00:10.200","Text":"Electromagnetic waves, which are things like visible light,"},{"Start":"00:10.200 ","End":"00:14.415","Text":"microwaves, or x-rays can travel through a vacuum."},{"Start":"00:14.415 ","End":"00:17.805","Text":"In this respect, they\u0027re quite different from sound waves"},{"Start":"00:17.805 ","End":"00:21.135","Text":"that can only travel in a medium where there are particles."},{"Start":"00:21.135 ","End":"00:23.910","Text":"Sound waves can travel in air,"},{"Start":"00:23.910 ","End":"00:30.209","Text":"but cannot travel say from the sun to the beginning of the Earth\u0027s atmosphere."},{"Start":"00:30.209 ","End":"00:34.545","Text":"Whereas electromagnetic waves can travel from the sun."},{"Start":"00:34.545 ","End":"00:38.965","Text":"Now, as you would expect for the title electromagnetic,"},{"Start":"00:38.965 ","End":"00:42.799","Text":"there are both electric and magnetic components involved."},{"Start":"00:42.799 ","End":"00:44.480","Text":"Let\u0027s illustrate this."},{"Start":"00:44.480 ","End":"00:47.105","Text":"Before we look at this illustration,"},{"Start":"00:47.105 ","End":"00:50.270","Text":"let\u0027s draw some coordinates."},{"Start":"00:50.270 ","End":"00:53.690","Text":"Let\u0027s consider this as the x coordinate,"},{"Start":"00:53.690 ","End":"00:57.440","Text":"y coordinate, and z coordinate."},{"Start":"00:57.440 ","End":"00:59.465","Text":"Now let\u0027s look at the picture."},{"Start":"00:59.465 ","End":"01:04.895","Text":"Light travels in a straight line."},{"Start":"01:04.895 ","End":"01:07.370","Text":"We\u0027ll call this the x direction."},{"Start":"01:07.370 ","End":"01:10.280","Text":"That\u0027s the direction in which the light travels."},{"Start":"01:10.280 ","End":"01:13.295","Text":"Associated with this direction,"},{"Start":"01:13.295 ","End":"01:16.775","Text":"there are 2 fields, 2 waves."},{"Start":"01:16.775 ","End":"01:18.470","Text":"There is electric wave,"},{"Start":"01:18.470 ","End":"01:21.415","Text":"which we\u0027ve drawn here in red,"},{"Start":"01:21.415 ","End":"01:23.390","Text":"and a magnetic wave,"},{"Start":"01:23.390 ","End":"01:25.255","Text":"which I\u0027ve drawn here in purple."},{"Start":"01:25.255 ","End":"01:30.605","Text":"Now, the electric and magnetic waves are at right angles to each other."},{"Start":"01:30.605 ","End":"01:33.665","Text":"If the light is traveling in the x-direction,"},{"Start":"01:33.665 ","End":"01:40.250","Text":"in this picture, the electric wave is drawn in the xz plane."},{"Start":"01:40.250 ","End":"01:45.055","Text":"The magnetic field is drawn in the xy plane,"},{"Start":"01:45.055 ","End":"01:47.595","Text":"right angles to each other."},{"Start":"01:47.595 ","End":"01:49.485","Text":"Now, let\u0027s look at the waves."},{"Start":"01:49.485 ","End":"01:52.570","Text":"First, let\u0027s look at the red wave."},{"Start":"01:52.570 ","End":"01:56.990","Text":"We see that first of all, it goes up,"},{"Start":"01:56.990 ","End":"02:01.295","Text":"it increases and then decreases reaching 0,"},{"Start":"02:01.295 ","End":"02:03.415","Text":"then becomes negative,"},{"Start":"02:03.415 ","End":"02:07.910","Text":"decreases and then increases reaching again 0."},{"Start":"02:07.910 ","End":"02:11.810","Text":"Its behavior is what we\u0027d call sinusoidal."},{"Start":"02:11.810 ","End":"02:16.320","Text":"It behaves like a sine function."},{"Start":"02:19.520 ","End":"02:28.535","Text":"At right angles to it is the magnetic wave and it behaves also as a sinusoidal wave,"},{"Start":"02:28.535 ","End":"02:30.545","Text":"like a sine function."},{"Start":"02:30.545 ","End":"02:34.700","Text":"We see that they are both had the same argument because"},{"Start":"02:34.700 ","End":"02:38.900","Text":"they reach 0 at precisely the same place."},{"Start":"02:38.900 ","End":"02:42.515","Text":"Now every wave like this, every wave,"},{"Start":"02:42.515 ","End":"02:47.930","Text":"which is electric or magnetic component, has a wavelength."},{"Start":"02:47.930 ","End":"02:53.870","Text":"The wavelength is the distance between 2 maxima or between 2 minima."},{"Start":"02:53.870 ","End":"02:57.845","Text":"We\u0027ll see in the next video that every range of"},{"Start":"02:57.845 ","End":"03:04.475","Text":"electromagnetic radiation visible light or infrared,"},{"Start":"03:04.475 ","End":"03:10.850","Text":"or x-rays, each one has a different lambda, a different wavelength."},{"Start":"03:10.850 ","End":"03:15.845","Text":"The wavelength lambda is the distance between 2 maxima or 2 minima,"},{"Start":"03:15.845 ","End":"03:18.124","Text":"and the units are in meters."},{"Start":"03:18.124 ","End":"03:25.120","Text":"Sometimes we use components on meters like nanometers or millimeters."},{"Start":"03:25.120 ","End":"03:31.265","Text":"Now, not only is the wavelength but there is also a frequency and the two are related."},{"Start":"03:31.265 ","End":"03:33.530","Text":"What\u0027s the frequency?"},{"Start":"03:33.530 ","End":"03:39.560","Text":"If I were to stand at a particular point and watch this wave passing me."},{"Start":"03:39.560 ","End":"03:45.310","Text":"Then, every time a minimum passed me, I will count."},{"Start":"03:45.310 ","End":"03:50.390","Text":"I would count the number of times in a second that the minimum passes me."},{"Start":"03:50.390 ","End":"03:52.220","Text":"That\u0027s called the frequency."},{"Start":"03:52.220 ","End":"03:55.340","Text":"If our standard point, What\u0027s the waves pass me the number of times a"},{"Start":"03:55.340 ","End":"03:59.809","Text":"maximum or minimum passes me in a second is called the frequency."},{"Start":"03:59.809 ","End":"04:05.005","Text":"We use the Greek letter Nu for the frequency."},{"Start":"04:05.005 ","End":"04:11.435","Text":"The units are seconds minus 1 because we\u0027re measuring in every second."},{"Start":"04:11.435 ","End":"04:16.480","Text":"Nowadays, we call this Hertz and written Hz."},{"Start":"04:16.480 ","End":"04:20.750","Text":"Now, what\u0027s the connection between the wavelength and frequency?"},{"Start":"04:20.750 ","End":"04:24.620","Text":"In a vacuum for electromagnetic radiation,"},{"Start":"04:24.620 ","End":"04:27.560","Text":"lambda, the wavelength times Nu,"},{"Start":"04:27.560 ","End":"04:29.690","Text":"the frequency is equal to c,"},{"Start":"04:29.690 ","End":"04:34.110","Text":"where c is the speed of light in a vacuum and it\u0027s equal to"},{"Start":"04:34.110 ","End":"04:39.290","Text":"2.9979 times 10 to the power of 8 meters per second,"},{"Start":"04:39.290 ","End":"04:45.445","Text":"which we\u0027ll write here as 3.00 times 10 to the power 8 meters per second."},{"Start":"04:45.445 ","End":"04:47.990","Text":"This is a universal constant."},{"Start":"04:47.990 ","End":"04:50.300","Text":"All radiation in vacuum,"},{"Start":"04:50.300 ","End":"04:54.410","Text":"all electromagnetic radiation in a vacuum travels at"},{"Start":"04:54.410 ","End":"04:59.750","Text":"precisely the same speed and this speed cannot be exceeded."},{"Start":"04:59.750 ","End":"05:04.175","Text":"Let\u0027s take an example of the connection between lambda,"},{"Start":"05:04.175 ","End":"05:07.205","Text":"the wavelength, and Nu the frequency."},{"Start":"05:07.205 ","End":"05:11.285","Text":"If red visible light has a wavelength of 700 nanometers,"},{"Start":"05:11.285 ","End":"05:13.190","Text":"what is its frequency?"},{"Start":"05:13.190 ","End":"05:18.455","Text":"Now we know that lambda times nu is equal to c,"},{"Start":"05:18.455 ","End":"05:22.625","Text":"nu is equal to c over lambda."},{"Start":"05:22.625 ","End":"05:29.375","Text":"Nu is equal to c over lambda c is 3.00 times 10 to the power 8 meters per second."},{"Start":"05:29.375 ","End":"05:35.410","Text":"Lambda is 700 times 10 to the power minus 9 meters."},{"Start":"05:35.410 ","End":"05:37.155","Text":"This is for nanometer,"},{"Start":"05:37.155 ","End":"05:39.210","Text":"10 to the power minus 9."},{"Start":"05:39.210 ","End":"05:46.800","Text":"Now, we can write 700 times 10 to the power minus 9 as 7 times 10 to the power minus 7."},{"Start":"05:46.800 ","End":"05:51.270","Text":"If we divide 3 by 7, we get 0.429."},{"Start":"05:51.270 ","End":"05:56.160","Text":"If divide 10 power 8 by 10 to the power minus 7,"},{"Start":"05:56.160 ","End":"05:59.110","Text":"we get 10 to the power of 50."},{"Start":"05:59.120 ","End":"06:02.325","Text":"Meters cancels with meters."},{"Start":"06:02.325 ","End":"06:05.535","Text":"We\u0027re left with seconds to power minus 1,"},{"Start":"06:05.535 ","End":"06:08.205","Text":"which we said or called hertz."},{"Start":"06:08.205 ","End":"06:13.700","Text":"The answer is 0.429 times 10 to the power of 15 hertz."},{"Start":"06:13.700 ","End":"06:21.290","Text":"We can write that in a more usual form 4.29 times 10 to the power 14 hertz."},{"Start":"06:21.290 ","End":"06:23.740","Text":"That\u0027s the answer to our question."},{"Start":"06:23.740 ","End":"06:30.065","Text":"That\u0027s the frequency of light that has a wavelength of 700 nanometers,"},{"Start":"06:30.065 ","End":"06:32.030","Text":"a very large number."},{"Start":"06:32.030 ","End":"06:37.080","Text":"This video, we talked about electromagnetic radiation."}],"ID":20864},{"Watched":false,"Name":"Electromagnetic Spectrum","Duration":"3m 53s","ChapterTopicVideoID":20096,"CourseChapterTopicPlaylistID":154565,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20096.jpeg","UploadDate":"2019-07-10T23:04:08.3430000","DurationForVideoObject":"PT3M53S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.950","Text":"In the previous video,"},{"Start":"00:01.950 ","End":"00:04.515","Text":"we describe electromagnetic waves."},{"Start":"00:04.515 ","End":"00:08.490","Text":"In this video, we\u0027ll discuss electromagnetic spectrum."},{"Start":"00:08.490 ","End":"00:10.740","Text":"What\u0027s the electromagnetic spectrum?"},{"Start":"00:10.740 ","End":"00:13.650","Text":"Electromagnetic spectrum is the range of values of"},{"Start":"00:13.650 ","End":"00:17.595","Text":"the frequency and wavelength of electromagnetic waves."},{"Start":"00:17.595 ","End":"00:20.085","Text":"Here\u0027s a diagram of the spectrum."},{"Start":"00:20.085 ","End":"00:22.365","Text":"At the top we have a wave,"},{"Start":"00:22.365 ","End":"00:26.865","Text":"whose wavelength is constantly increasing from left to right."},{"Start":"00:26.865 ","End":"00:29.880","Text":"That\u0027s just to tell us that in this diagram,"},{"Start":"00:29.880 ","End":"00:33.870","Text":"the wavelength will increase as we go from left to right."},{"Start":"00:33.870 ","End":"00:35.310","Text":"If this is true,"},{"Start":"00:35.310 ","End":"00:42.045","Text":"then the frequency must decrease as we go from left to right with the right like that."},{"Start":"00:42.045 ","End":"00:44.614","Text":"Because as we learned before,"},{"Start":"00:44.614 ","End":"00:51.050","Text":"the frequency is equal to the speed of light divided by the wavelength."},{"Start":"00:51.050 ","End":"00:53.765","Text":"They\u0027re inversely proportional."},{"Start":"00:53.765 ","End":"00:57.440","Text":"Let\u0027s begin by looking at the left-hand part of"},{"Start":"00:57.440 ","End":"01:01.520","Text":"the diagram where we have gamma rays and x-rays."},{"Start":"01:01.520 ","End":"01:05.360","Text":"These have short wavelengths and high frequencies."},{"Start":"01:05.360 ","End":"01:09.595","Text":"X-rays are used to study crystals because"},{"Start":"01:09.595 ","End":"01:17.150","Text":"their wavelength is somewhat similar to the distance between the atoms in crystals."},{"Start":"01:17.150 ","End":"01:22.100","Text":"Gamma rays are often used in science fiction,"},{"Start":"01:22.100 ","End":"01:27.050","Text":"because they are emitted from radioactive substances."},{"Start":"01:27.050 ","End":"01:30.800","Text":"Now let\u0027s look at the other side of the spectrum,"},{"Start":"01:30.800 ","End":"01:34.490","Text":"where we have long wavelengths and low frequencies."},{"Start":"01:34.490 ","End":"01:39.275","Text":"Here we have microwaves and radio waves, also television waves."},{"Start":"01:39.275 ","End":"01:43.640","Text":"For example, the frequency of the standard microwave oven is"},{"Start":"01:43.640 ","End":"01:50.345","Text":"2.45 gigahertz and it\u0027s wavelength is about 12 centimeters,"},{"Start":"01:50.345 ","End":"01:52.475","Text":"which is rather large."},{"Start":"01:52.475 ","End":"01:58.960","Text":"We always use this frequency so as not to interfere with telecommunications."},{"Start":"01:58.960 ","End":"02:01.414","Text":"Now in the central part of the spectrum,"},{"Start":"02:01.414 ","End":"02:03.410","Text":"we have the visible range."},{"Start":"02:03.410 ","End":"02:08.825","Text":"Now here it\u0027s magnified because it\u0027s really a tiny part of the whole spectrum."},{"Start":"02:08.825 ","End":"02:10.940","Text":"This is all that we can see,"},{"Start":"02:10.940 ","End":"02:12.755","Text":"all that humans can see."},{"Start":"02:12.755 ","End":"02:17.930","Text":"It goes from Lambda equal to 390 nanometers."},{"Start":"02:17.930 ","End":"02:19.370","Text":"Nanometers, if you remember,"},{"Start":"02:19.370 ","End":"02:22.670","Text":"is 10^-9 meters,"},{"Start":"02:23.140 ","End":"02:26.945","Text":"up to 760 nanometers."},{"Start":"02:26.945 ","End":"02:35.320","Text":"The left it goes from violet to blue through the other colors \u0027till it gets to red."},{"Start":"02:35.320 ","End":"02:41.020","Text":"Blue light is of shorter wavelength than red light."},{"Start":"02:41.020 ","End":"02:43.505","Text":"When you see white light,"},{"Start":"02:43.505 ","End":"02:47.029","Text":"it\u0027s really just a mixture of all these colors."},{"Start":"02:47.029 ","End":"02:48.865","Text":"They\u0027re all mixed up."},{"Start":"02:48.865 ","End":"02:52.205","Text":"If it pass white light through a glass prism,"},{"Start":"02:52.205 ","End":"02:55.085","Text":"it is dispersed into the different colors."},{"Start":"02:55.085 ","End":"02:59.900","Text":"We all know this because the same happens when sunlight is dispersed by"},{"Start":"02:59.900 ","End":"03:05.420","Text":"water droplets in the atmosphere or in a waterfall and we see a rainbow."},{"Start":"03:05.420 ","End":"03:08.630","Text":"We see the rainbow of colors, all the colors."},{"Start":"03:08.630 ","End":"03:12.930","Text":"Now to the left of the visible spectrum,"},{"Start":"03:12.930 ","End":"03:19.985","Text":"that means that the wavelength smaller than Lambda equal to 390 nanometers."},{"Start":"03:19.985 ","End":"03:22.160","Text":"We have beyond the blue,"},{"Start":"03:22.160 ","End":"03:24.980","Text":"which we call ultraviolet UV."},{"Start":"03:24.980 ","End":"03:29.385","Text":"It wavelengths greater than 760 nanometers."},{"Start":"03:29.385 ","End":"03:33.455","Text":"Beyond the red, we have what we call infrared."},{"Start":"03:33.455 ","End":"03:38.375","Text":"This is the ultraviolet range and the infrared range."},{"Start":"03:38.375 ","End":"03:43.505","Text":"Here\u0027s the ultraviolet Lambda less than 390 nanometers,"},{"Start":"03:43.505 ","End":"03:48.125","Text":"and infrared Lambda great than 760 nanometers."},{"Start":"03:48.125 ","End":"03:53.280","Text":"In this video, we talked about the electromagnetic spectrum."}],"ID":20865},{"Watched":false,"Name":"Interference between Waves","Duration":"4m 38s","ChapterTopicVideoID":20097,"CourseChapterTopicPlaylistID":154565,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20097.jpeg","UploadDate":"2019-07-10T23:03:08.7500000","DurationForVideoObject":"PT4M38S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.545","Text":"In a previous video,"},{"Start":"00:01.545 ","End":"00:03.960","Text":"we learned about electromagnetic waves."},{"Start":"00:03.960 ","End":"00:07.935","Text":"In this video, we\u0027ll talk about the interference between waves."},{"Start":"00:07.935 ","End":"00:10.860","Text":"Let\u0027s start with constructive interference."},{"Start":"00:10.860 ","End":"00:13.214","Text":"In this picture, I\u0027ve drawn 2 waves,"},{"Start":"00:13.214 ","End":"00:18.060","Text":"a blue one and the red one and they each have the same wavelength."},{"Start":"00:18.060 ","End":"00:21.225","Text":"That\u0027s the distance from here to here, from here to here."},{"Start":"00:21.225 ","End":"00:26.310","Text":"Then in addition, they have the same maximum amplitude."},{"Start":"00:26.310 ","End":"00:30.015","Text":"That\u0027s the height of the peak above 0."},{"Start":"00:30.015 ","End":"00:36.330","Text":"These 2 waves are said to be in phase because"},{"Start":"00:36.330 ","End":"00:39.090","Text":"the maximum in this one and"},{"Start":"00:39.090 ","End":"00:43.339","Text":"the maximum in the second one are in precisely the same place."},{"Start":"00:43.339 ","End":"00:46.190","Text":"The minimum in this one and the minimum in"},{"Start":"00:46.190 ","End":"00:49.400","Text":"the second one are in precisely the same place."},{"Start":"00:49.400 ","End":"00:53.550","Text":"These are said to be in phase."},{"Start":"00:55.820 ","End":"00:58.995","Text":"When we add them up,"},{"Start":"00:58.995 ","End":"01:08.360","Text":"we get something which has the same wavelength and an amplitude above 0,"},{"Start":"01:08.360 ","End":"01:10.070","Text":"which is twice as much."},{"Start":"01:10.070 ","End":"01:12.205","Text":"You can see that it\u0027s 2."},{"Start":"01:12.205 ","End":"01:15.705","Text":"Here, it\u0027s 2 and here it\u0027s 1 and 1."},{"Start":"01:15.705 ","End":"01:17.610","Text":"When this happens,"},{"Start":"01:17.610 ","End":"01:22.250","Text":"we get what we call constructive interference."},{"Start":"01:22.250 ","End":"01:25.700","Text":"If 2 waves with the same wavelength and amplitude are"},{"Start":"01:25.700 ","End":"01:29.420","Text":"aligned so that the maxima and minima coincide,"},{"Start":"01:29.420 ","End":"01:32.480","Text":"the waves are said to be in phase."},{"Start":"01:32.480 ","End":"01:34.070","Text":"When we add the waves,"},{"Start":"01:34.070 ","End":"01:40.235","Text":"we get constructive interference and the amplitude is twice that of the individual waves."},{"Start":"01:40.235 ","End":"01:44.645","Text":"Now, we\u0027re going to talk about destructive interference."},{"Start":"01:44.645 ","End":"01:49.730","Text":"Here we have the same blue wave as before,"},{"Start":"01:49.730 ","End":"01:54.860","Text":"but I\u0027ve taken the red wave and moved it by Pi."},{"Start":"01:54.860 ","End":"02:01.250","Text":"The maximum instead of being at Pi here, here is 2Pi."},{"Start":"02:01.250 ","End":"02:03.680","Text":"I have moved it by Pi."},{"Start":"02:03.680 ","End":"02:07.395","Text":"Now, when we add the two together,"},{"Start":"02:07.395 ","End":"02:13.750","Text":"here we\u0027re adding a maximum of plus 1 together with a minimum of minus 1,"},{"Start":"02:13.750 ","End":"02:16.430","Text":"so the answer is 0."},{"Start":"02:16.430 ","End":"02:20.150","Text":"Every place we do this, we\u0027ll get 0."},{"Start":"02:20.150 ","End":"02:24.190","Text":"This is called destructive interference."},{"Start":"02:24.190 ","End":"02:31.050","Text":"Now, we say that the waves are out of phase or out of phase by Pi,"},{"Start":"02:31.050 ","End":"02:38.245","Text":"because I have moved the second one by Pi so that a maximum corresponds to a minimum."},{"Start":"02:38.245 ","End":"02:41.740","Text":"These are out of phase."},{"Start":"02:44.290 ","End":"02:47.045","Text":"When the waves are out of phase,"},{"Start":"02:47.045 ","End":"02:52.830","Text":"we get destructive interference and I\u0027ve written it out here."},{"Start":"02:55.310 ","End":"02:59.900","Text":"If 2 waves with the same wavelength and amplitude are aligned so that"},{"Start":"02:59.900 ","End":"03:03.640","Text":"the maximum of one coincides with the minimum the other,"},{"Start":"03:03.640 ","End":"03:06.955","Text":"the waves are said to be out of phase."},{"Start":"03:06.955 ","End":"03:08.420","Text":"When we add the waves,"},{"Start":"03:08.420 ","End":"03:13.355","Text":"we get destructive interference and the waves cancel each other."},{"Start":"03:13.355 ","End":"03:16.100","Text":"What about some examples?"},{"Start":"03:16.100 ","End":"03:19.055","Text":"Well, interference between all sorts of waves,"},{"Start":"03:19.055 ","End":"03:21.575","Text":"including electromagnetic waves,"},{"Start":"03:21.575 ","End":"03:24.150","Text":"occur all the time."},{"Start":"03:24.150 ","End":"03:27.530","Text":"There are many examples in everyday phenomena."},{"Start":"03:27.530 ","End":"03:30.680","Text":"One such example is the interference between the waves"},{"Start":"03:30.680 ","End":"03:34.100","Text":"formed when 2 stones are thrown into water."},{"Start":"03:34.100 ","End":"03:40.570","Text":"Supposing we have 2 stones thrown into water and there are ripples formed."},{"Start":"03:40.570 ","End":"03:42.620","Text":"Supposing here is the maximum of"},{"Start":"03:42.620 ","End":"03:48.380","Text":"a ripple in one and the maximum in the ripple of the other,"},{"Start":"03:48.380 ","End":"03:54.975","Text":"and another maximum here and maximum here."},{"Start":"03:54.975 ","End":"03:58.185","Text":"Now, the places where these 2 meet,"},{"Start":"03:58.185 ","End":"04:00.800","Text":"we\u0027ll get constructive interference."},{"Start":"04:00.800 ","End":"04:09.380","Text":"Now, supposing the maximum of one ripple meets the minimum of"},{"Start":"04:09.380 ","End":"04:19.485","Text":"the other ripple then the place where they meet will have destructive interference."},{"Start":"04:19.485 ","End":"04:24.650","Text":"We\u0027ll get a mixture of constructive and destructive interference,"},{"Start":"04:24.650 ","End":"04:28.400","Text":"and this will result in a very nice picture,"},{"Start":"04:28.400 ","End":"04:31.070","Text":"a very nice interference diagram."},{"Start":"04:31.070 ","End":"04:38.910","Text":"In this video, we discuss constructive and destructive interference between waves."}],"ID":20866}],"Thumbnail":null,"ID":154565},{"Name":"Atomic Spectra","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Atomic Spectra","Duration":"7m 32s","ChapterTopicVideoID":20092,"CourseChapterTopicPlaylistID":154566,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20092.jpeg","UploadDate":"2019-07-10T23:04:38.5470000","DurationForVideoObject":"PT7M32S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.710","Text":"In the previous video,"},{"Start":"00:01.710 ","End":"00:04.485","Text":"we talked about the electromagnetic spectrum."},{"Start":"00:04.485 ","End":"00:08.625","Text":"In this video, we\u0027ll talk about the spectra of various atoms."},{"Start":"00:08.625 ","End":"00:13.260","Text":"First, let\u0027s recall what we learned about the continuous spectrum of light."},{"Start":"00:13.260 ","End":"00:16.845","Text":"A continuous spectrum consists of many wavelengths."},{"Start":"00:16.845 ","End":"00:19.770","Text":"When there are many wavelengths close together,"},{"Start":"00:19.770 ","End":"00:23.490","Text":"we call it a continuum of wavelengths, continuum."},{"Start":"00:23.490 ","End":"00:26.475","Text":"Let\u0027s take an example of a continuous spectrum."},{"Start":"00:26.475 ","End":"00:29.355","Text":"Here is an old fashioned light bulb,"},{"Start":"00:29.355 ","End":"00:31.573","Text":"which has a filament inside it."},{"Start":"00:31.573 ","End":"00:34.860","Text":"When a current passes through it,"},{"Start":"00:34.860 ","End":"00:40.185","Text":"the filament glows and emits a continuous spectrum of colors,"},{"Start":"00:40.185 ","End":"00:43.595","Text":"so many colors that when they are mixed together,"},{"Start":"00:43.595 ","End":"00:46.460","Text":"they look as if they are white."},{"Start":"00:46.460 ","End":"00:48.725","Text":"The light emitted by the hot filament of"},{"Start":"00:48.725 ","End":"00:52.985","Text":"incandescent light bulb consists of many wavelengths."},{"Start":"00:52.985 ","End":"00:58.345","Text":"We can contrast this with a discrete or discontinuous spectrum."},{"Start":"00:58.345 ","End":"01:01.070","Text":"The visible spectrum emitted by atoms."},{"Start":"01:01.070 ","End":"01:03.290","Text":"We call this emission spectrum."},{"Start":"01:03.290 ","End":"01:07.910","Text":"Consists of a few discrete wavelengths, not a whole lot,"},{"Start":"01:07.910 ","End":"01:12.830","Text":"just a few and each element has its own distinctive spectrum,"},{"Start":"01:12.830 ","End":"01:18.120","Text":"which can be used to characterize it somewhat like a barcode."},{"Start":"01:18.710 ","End":"01:24.865","Text":"Except that here the barcode is colored and in the past and the 19th century,"},{"Start":"01:24.865 ","End":"01:30.220","Text":"several elements were identified in this way, cesium, rubidium."},{"Start":"01:30.220 ","End":"01:37.430","Text":"Rubidium, the name comes from the deep ride of Ruby and helium,"},{"Start":"01:37.430 ","End":"01:44.060","Text":"which was detected in the sun\u0027s spectrum a long time before it was detected on the earth."},{"Start":"01:44.060 ","End":"01:47.500","Text":"Helios is the Greek for sun."},{"Start":"01:47.500 ","End":"01:52.159","Text":"Let\u0027s talk about the spectra of the alkali elements."},{"Start":"01:52.159 ","End":"01:55.324","Text":"If you recall, the alkali elements are lithium,"},{"Start":"01:55.324 ","End":"02:02.190","Text":"sodium, potassium, rubidium, and cesium."},{"Start":"02:02.190 ","End":"02:05.360","Text":"Now when samples of lithium, sodium,"},{"Start":"02:05.360 ","End":"02:08.390","Text":"and potassium are heated in a gas flame,"},{"Start":"02:08.390 ","End":"02:12.290","Text":"the burner we call a bunsen burner you\u0027ve probably seen in your labs,"},{"Start":"02:12.290 ","End":"02:15.110","Text":"they emit red, orange, and purple light."},{"Start":"02:15.110 ","End":"02:17.420","Text":"Lithium emits red light,"},{"Start":"02:17.420 ","End":"02:20.015","Text":"sodium emits orange light,"},{"Start":"02:20.015 ","End":"02:22.535","Text":"and potassium emits purple light."},{"Start":"02:22.535 ","End":"02:25.205","Text":"Here we have our bunsen burner,"},{"Start":"02:25.205 ","End":"02:34.100","Text":"here\u0027s a flame you put into it a stick with a little sample of a compound containing,"},{"Start":"02:34.100 ","End":"02:39.900","Text":"for example, lithium, and then you see red emission."},{"Start":"02:40.600 ","End":"02:43.450","Text":"If you were to do it with sodium,"},{"Start":"02:43.450 ","End":"02:46.930","Text":"you would get orange and if you were to do it with potassium,"},{"Start":"02:46.930 ","End":"02:48.150","Text":"you will get purple."},{"Start":"02:48.150 ","End":"02:52.420","Text":"In fact, we have sodium fog lights you\u0027ve probably"},{"Start":"02:52.420 ","End":"02:59.095","Text":"seen and these are orange because inside the light,"},{"Start":"02:59.095 ","End":"03:02.094","Text":"there is some sodium gas."},{"Start":"03:02.094 ","End":"03:06.235","Text":"Now let\u0027s talk a little about the hydrogen spectrum."},{"Start":"03:06.235 ","End":"03:12.228","Text":"This is obtained by having a glass tube containing hydrogen."},{"Start":"03:12.228 ","End":"03:18.559","Text":"You pass a very strong electrical field through it 500 volts,"},{"Start":"03:18.770 ","End":"03:23.103","Text":"and it glows pink."},{"Start":"03:23.103 ","End":"03:29.900","Text":"When the spectrum is passed through a prism, you get lines."},{"Start":"03:29.900 ","End":"03:31.130","Text":"How many lines do you get?"},{"Start":"03:31.130 ","End":"03:33.605","Text":"You get 4 lines."},{"Start":"03:33.605 ","End":"03:37.685","Text":"The visible spectrum of hydrogen consists of 4 lines."},{"Start":"03:37.685 ","End":"03:41.900","Text":"There\u0027s a red line, 656 nanometers,"},{"Start":"03:41.900 ","End":"03:45.965","Text":"a greenish blue line at 486.1 nanometers,"},{"Start":"03:45.965 ","End":"03:50.440","Text":"and 2 purple lines at 434 and 410."},{"Start":"03:50.440 ","End":"03:53.015","Text":"Here\u0027s our red line,"},{"Start":"03:53.015 ","End":"03:55.975","Text":"and then our blue line,"},{"Start":"03:55.975 ","End":"03:59.450","Text":"and then our purple line,"},{"Start":"03:59.450 ","End":"04:06.330","Text":"except that they don\u0027t have a purple color so there\u0027s a 2 purple lines purple."},{"Start":"04:07.550 ","End":"04:11.750","Text":"Lambda increasing the wavelength increasing to the right."},{"Start":"04:11.750 ","End":"04:17.600","Text":"Notice that the lines become closer together as the wavelength decreases."},{"Start":"04:17.600 ","End":"04:22.895","Text":"The distance from red to blue is greater than the distance between blue to purple."},{"Start":"04:22.895 ","End":"04:27.380","Text":"In addition, there are other lines in the ultraviolet and infrared regions of"},{"Start":"04:27.380 ","End":"04:30.260","Text":"the spectrum but we can\u0027t see that with"},{"Start":"04:30.260 ","End":"04:34.775","Text":"our eyes the human eye cannot see ultraviolet or infrared."},{"Start":"04:34.775 ","End":"04:41.060","Text":"Now, Bomber managed to find a formula that explain these 4 lines."},{"Start":"04:41.060 ","End":"04:43.400","Text":"He did this in 1885."},{"Start":"04:43.400 ","End":"04:45.350","Text":"It was a simple empirical formula."},{"Start":"04:45.350 ","End":"04:47.890","Text":"That means he did it by trial and error."},{"Start":"04:47.890 ","End":"04:51.060","Text":"Translated into frequency here\u0027s this formula,"},{"Start":"04:51.060 ","End":"04:57.755","Text":"Nu the frequency is equal to 3.280 times 10^ 15 times"},{"Start":"04:57.755 ","End":"05:05.670","Text":"1 over 2 squared minus 1 over n squared and that\u0027s Hertz frequency in Hertz."},{"Start":"05:05.670 ","End":"05:08.595","Text":"If we substitute n equals 3,"},{"Start":"05:08.595 ","End":"05:10.245","Text":"we\u0027ll get the red line,"},{"Start":"05:10.245 ","End":"05:12.630","Text":"4 we\u0027ll get the blue line,"},{"Start":"05:12.630 ","End":"05:15.755","Text":"and 5 and 6 we\u0027ll get the 2 purple lines."},{"Start":"05:15.755 ","End":"05:19.460","Text":"Now, classical theory just can\u0027t explain this result."},{"Start":"05:19.460 ","End":"05:22.240","Text":"It can\u0027t explain why there are only 4 lines."},{"Start":"05:22.240 ","End":"05:25.295","Text":"It was explained many years later by Bohr in"},{"Start":"05:25.295 ","End":"05:29.300","Text":"1913 using a mixture of classical-quantum theory,"},{"Start":"05:29.300 ","End":"05:30.920","Text":"the new quantum theory,"},{"Start":"05:30.920 ","End":"05:37.475","Text":"and the venture was explained using just quantum theory sometime after 1927."},{"Start":"05:37.475 ","End":"05:43.090","Text":"Let\u0027s take an example of the use of Balmer\u0027s equation. Here\u0027s the question."},{"Start":"05:43.090 ","End":"05:46.880","Text":"Show that the red line in the hydrogen spectrum is obtained by"},{"Start":"05:46.880 ","End":"05:50.926","Text":"substituting n equal to 3 in the Balmer\u0027s formula."},{"Start":"05:50.926 ","End":"05:53.525","Text":"Here\u0027s our equation as we had before."},{"Start":"05:53.525 ","End":"05:56.940","Text":"If we calculate 1 over 2 squared,"},{"Start":"05:56.940 ","End":"06:01.440","Text":"which of course is 1/4 or 1/4 minus 1/3 squared,"},{"Start":"06:01.440 ","End":"06:09.660","Text":"which is 1/9 multiply by 3.2881 times 10 to power 15 you get the answer,"},{"Start":"06:09.660 ","End":"06:15.540","Text":"4.5668 times 10^ 14 Hertz"},{"Start":"06:15.540 ","End":"06:20.630","Text":"but this is frequency and we want wavelengths,"},{"Start":"06:20.630 ","End":"06:25.060","Text":"so we have to calculate the wavelength from this frequency."},{"Start":"06:25.060 ","End":"06:28.810","Text":"Remember from previous video that Lambda,"},{"Start":"06:28.810 ","End":"06:30.500","Text":"the wavelength is equal to c,"},{"Start":"06:30.500 ","End":"06:34.680","Text":"the speed of light divided by the frequency the speed of light is"},{"Start":"06:34.680 ","End":"06:39.660","Text":"2.9979 times 10^ 8 meters per second,"},{"Start":"06:39.660 ","End":"06:45.535","Text":"and the frequency is 4.5668 times 10^ 14 Hertz."},{"Start":"06:45.535 ","End":"06:49.890","Text":"Hertz is also seconds to power minus 1."},{"Start":"06:49.890 ","End":"06:52.400","Text":"When we divide these,"},{"Start":"06:52.400 ","End":"07:02.645","Text":"we get 6.564106 times 10^ minus 7 meters and we have to translate that into nanometers."},{"Start":"07:02.645 ","End":"07:08.870","Text":"We can write that as 656.5 times 10^ minus"},{"Start":"07:08.870 ","End":"07:13.470","Text":"9 meters and 10^ minus n9 is"},{"Start":"07:13.470 ","End":"07:20.230","Text":"a nanometer so our answer is 656.5 nanometers."},{"Start":"07:21.500 ","End":"07:25.970","Text":"In this video, we talked about atomic spectra,"},{"Start":"07:25.970 ","End":"07:31.440","Text":"but discrete spectra as opposed to continuous spectrum."}],"ID":20863},{"Watched":false,"Name":"Exercise 1","Duration":"3m 23s","ChapterTopicVideoID":22933,"CourseChapterTopicPlaylistID":154566,"HasSubtitles":false,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22933.jpeg","UploadDate":"2020-12-16T03:28:14.3900000","DurationForVideoObject":"PT3M23S","Description":null,"VideoComments":[],"Subtitles":[],"ID":23754},{"Watched":false,"Name":"Exercise 2","Duration":"3m 44s","ChapterTopicVideoID":22932,"CourseChapterTopicPlaylistID":154566,"HasSubtitles":false,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22932.jpeg","UploadDate":"2020-12-16T03:28:05.3100000","DurationForVideoObject":"PT3M44S","Description":null,"VideoComments":[],"Subtitles":[],"ID":23753}],"Thumbnail":null,"ID":154566},{"Name":"Quantum Theory","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Planck\u0027s Equation","Duration":"7m 7s","ChapterTopicVideoID":20093,"CourseChapterTopicPlaylistID":154567,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20093.jpeg","UploadDate":"2019-05-30T01:54:33.7800000","DurationForVideoObject":"PT7M7S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.500","Text":"In the previous video,"},{"Start":"00:01.500 ","End":"00:03.975","Text":"we talked about atomic spectra."},{"Start":"00:03.975 ","End":"00:05.880","Text":"In this video, we\u0027ll talk about"},{"Start":"00:05.880 ","End":"00:09.975","Text":"another phenomenon that cannot be explained by classical theory."},{"Start":"00:09.975 ","End":"00:12.915","Text":"It\u0027s called black body radiation."},{"Start":"00:12.915 ","End":"00:16.635","Text":"Here are a few facts about black body radiation."},{"Start":"00:16.635 ","End":"00:18.840","Text":"The first thing to notice, all bodies,"},{"Start":"00:18.840 ","End":"00:22.185","Text":"including the human body, emit radiation."},{"Start":"00:22.185 ","End":"00:24.585","Text":"At room temperature, we emit"},{"Start":"00:24.585 ","End":"00:31.185","Text":"infrared radiation and that\u0027s why night goggles can be used to find people in the dark."},{"Start":"00:31.185 ","End":"00:34.380","Text":"When an iron poker is put into a fire it"},{"Start":"00:34.380 ","End":"00:38.115","Text":"acquires a color that depends only on its temperature."},{"Start":"00:38.115 ","End":"00:39.480","Text":"It goes from red,"},{"Start":"00:39.480 ","End":"00:41.465","Text":"that\u0027s what we mean by red hot,"},{"Start":"00:41.465 ","End":"00:43.470","Text":"to yellow to white,"},{"Start":"00:43.470 ","End":"00:46.100","Text":"and that\u0027s what we mean by white-hot."},{"Start":"00:46.100 ","End":"00:49.175","Text":"This is often called black body radiation."},{"Start":"00:49.175 ","End":"00:56.465","Text":"A black body is an object that absorbs and emits radiation of all frequencies uniformly."},{"Start":"00:56.465 ","End":"01:00.710","Text":"If you shine light of all different frequencies on a black body,"},{"Start":"01:00.710 ","End":"01:02.689","Text":"it will absorb everything."},{"Start":"01:02.689 ","End":"01:07.055","Text":"Now let\u0027s look at the spectrum of radiation emitted by a black body."},{"Start":"01:07.055 ","End":"01:09.605","Text":"Here\u0027s what\u0027s found experimentally."},{"Start":"01:09.605 ","End":"01:13.910","Text":"We see a distribution of wavelengths."},{"Start":"01:13.910 ","End":"01:16.980","Text":"If the temperature is 6,000 Kelvin,"},{"Start":"01:16.980 ","End":"01:18.510","Text":"which is very, very hot,"},{"Start":"01:18.510 ","End":"01:20.310","Text":"hotter than the sun,"},{"Start":"01:20.310 ","End":"01:25.670","Text":"then the maximum falls in the region of the blue light,"},{"Start":"01:25.670 ","End":"01:27.140","Text":"so it will look blue."},{"Start":"01:27.140 ","End":"01:31.055","Text":"This is 1 of the ways to find the temperature of a star."},{"Start":"01:31.055 ","End":"01:33.255","Text":"If the temperature is 6,000 Kelvin,"},{"Start":"01:33.255 ","End":"01:35.000","Text":"they know it\u0027s a blue star."},{"Start":"01:35.000 ","End":"01:41.190","Text":"At 5,500 Kelvin, we get green and at 4,000 Kelvin,"},{"Start":"01:41.190 ","End":"01:43.290","Text":"the maximum is at red."},{"Start":"01:43.290 ","End":"01:46.115","Text":"Now, this distribution of wavelengths"},{"Start":"01:46.115 ","End":"01:49.310","Text":"has a maximum that depends only on the temperature,"},{"Start":"01:49.310 ","End":"01:53.030","Text":"and no classical theory could explain this behavior."},{"Start":"01:53.030 ","End":"01:56.750","Text":"One of the downfalls of the classical theory is what\u0027s"},{"Start":"01:56.750 ","End":"02:00.425","Text":"called the ultraviolet catastrophe. What does that mean?"},{"Start":"02:00.425 ","End":"02:04.250","Text":"The classical theory, instead of giving a curve that has"},{"Start":"02:04.250 ","End":"02:11.220","Text":"a maximum and looks very much like Maxwell-Boltzmann that we learned about before."},{"Start":"02:16.540 ","End":"02:20.120","Text":"Very much like Maxwell-Boltzmann distribution,"},{"Start":"02:20.120 ","End":"02:24.590","Text":"classical theory gives us something just continuous going further and"},{"Start":"02:24.590 ","End":"02:29.195","Text":"further up at law wavelengths."},{"Start":"02:29.195 ","End":"02:32.540","Text":"Low wavelengths means high frequencies."},{"Start":"02:32.540 ","End":"02:34.130","Text":"It gets higher and higher and higher,"},{"Start":"02:34.130 ","End":"02:35.780","Text":"never curves over,"},{"Start":"02:35.780 ","End":"02:37.760","Text":"and starts to decrease again."},{"Start":"02:37.760 ","End":"02:41.135","Text":"This is called the ultraviolet catastrophe"},{"Start":"02:41.135 ","End":"02:45.695","Text":"because the amount of radiation and the ultraviolet is enormous."},{"Start":"02:45.695 ","End":"02:47.975","Text":"It\u0027s infinite, according to this."},{"Start":"02:47.975 ","End":"02:53.560","Text":"The classical theory say the intensity of light increases as the wavelength decreases,"},{"Start":"02:53.560 ","End":"02:56.555","Text":"and we call it the ultraviolet catastrophe."},{"Start":"02:56.555 ","End":"03:01.505","Text":"In fact, a consequence of this is that according to classical theory,"},{"Start":"03:01.505 ","End":"03:03.980","Text":"all objects should glow in the dark."},{"Start":"03:03.980 ","End":"03:07.825","Text":"There should really be no dark because everything is glowing."},{"Start":"03:07.825 ","End":"03:10.010","Text":"Now, in the 19th century,"},{"Start":"03:10.010 ","End":"03:12.260","Text":"there were many attempts to solve the problem."},{"Start":"03:12.260 ","End":"03:16.895","Text":"Many attempts to understand why you should get such a distribution."},{"Start":"03:16.895 ","End":"03:20.620","Text":"The person who solves the problem was called Planck."},{"Start":"03:20.620 ","End":"03:27.560","Text":"He did it in 1900 and later got the Nobel Prize for it in 1980."},{"Start":"03:27.560 ","End":"03:29.555","Text":"He made a hypothesis."},{"Start":"03:29.555 ","End":"03:31.745","Text":"A hypothesis is an assumption."},{"Start":"03:31.745 ","End":"03:34.855","Text":"Now, he made this hypothesis;"},{"Start":"03:34.855 ","End":"03:36.420","Text":"I\u0027ll describe in a minute,"},{"Start":"03:36.420 ","End":"03:39.560","Text":"and using it, derived to the expression that"},{"Start":"03:39.560 ","End":"03:43.175","Text":"fitted just exactly the graphs that we had before."},{"Start":"03:43.175 ","End":"03:46.010","Text":"This is called the Planck distribution."},{"Start":"03:46.010 ","End":"03:53.270","Text":"In fact, I used the expression of the Planck distribution to reproduce the graphs above."},{"Start":"03:53.270 ","End":"03:57.718","Text":"Now, he was coming after many people who had tried before."},{"Start":"03:57.718 ","End":"04:00.170","Text":"Like Lord Rayleigh who came before him,"},{"Start":"04:00.170 ","End":"04:02.810","Text":"he assumed that the electromagnetic field"},{"Start":"04:02.810 ","End":"04:06.830","Text":"consists of electromagnetic oscillators of all frequencies."},{"Start":"04:06.830 ","End":"04:10.520","Text":"Electromagnetic field is all different oscillators."},{"Start":"04:10.520 ","End":"04:13.100","Text":"One in one frequency,"},{"Start":"04:13.100 ","End":"04:15.840","Text":"another one in another frequency, and so on."},{"Start":"04:15.970 ","End":"04:19.970","Text":"However, unlike Rayleigh,"},{"Start":"04:19.970 ","End":"04:23.150","Text":"he assumed that the energy of an oscillator of frequency"},{"Start":"04:23.150 ","End":"04:26.885","Text":"v can only come in multiples of hv,"},{"Start":"04:26.885 ","End":"04:29.420","Text":"come in little bundles of hv."},{"Start":"04:29.420 ","End":"04:33.770","Text":"That he wrote that the energy is equal to n,"},{"Start":"04:33.770 ","End":"04:37.840","Text":"that\u0027s the number of bundles of each v,"},{"Start":"04:37.840 ","End":"04:40.009","Text":"and each has a constant,"},{"Start":"04:40.009 ","End":"04:42.530","Text":"which is now called Planck\u0027s constant,"},{"Start":"04:42.530 ","End":"04:44.090","Text":"I\u0027ll describe it in the net,"},{"Start":"04:44.090 ","End":"04:46.475","Text":"times nu, the frequency."},{"Start":"04:46.475 ","End":"04:48.770","Text":"The energy is proportional to the frequency."},{"Start":"04:48.770 ","End":"04:49.880","Text":"The higher the frequency,"},{"Start":"04:49.880 ","End":"04:51.800","Text":"the higher the energy."},{"Start":"04:51.800 ","End":"04:56.270","Text":"Now, Planck\u0027s constant is a very small number."},{"Start":"04:56.270 ","End":"04:58.610","Text":"That\u0027s why we don\u0027t see it,"},{"Start":"04:58.610 ","End":"05:01.595","Text":"only in microscopic phenomena."},{"Start":"05:01.595 ","End":"05:11.119","Text":"H is equal to 6.62608 times 10^minus 34 joules times second."},{"Start":"05:11.119 ","End":"05:15.380","Text":"That\u0027s Planck\u0027s constant, which is the universal constant."},{"Start":"05:15.380 ","End":"05:17.150","Text":"We\u0027ll see it many times."},{"Start":"05:17.150 ","End":"05:20.045","Text":"Then we have Planck\u0027s equation."},{"Start":"05:20.045 ","End":"05:29.090","Text":"It says that energy of a unit of electromagnetic radiation is equal to h,"},{"Start":"05:29.090 ","End":"05:30.230","Text":"that is Planck\u0027s constant,"},{"Start":"05:30.230 ","End":"05:32.405","Text":"times nu, the frequency."},{"Start":"05:32.405 ","End":"05:36.410","Text":"Each unit, each bundle of energy is called a quantum."},{"Start":"05:36.410 ","End":"05:41.225","Text":"Nowadays, a quantum of electromagnetic radiation is called a photon."},{"Start":"05:41.225 ","End":"05:43.879","Text":"Photon for the word for light."},{"Start":"05:43.879 ","End":"05:47.570","Text":"The energy of a photon is proportional to its frequency,"},{"Start":"05:47.570 ","End":"05:52.955","Text":"and the intensity of electromagnetic radiation is proportional to the number of photons."},{"Start":"05:52.955 ","End":"05:56.780","Text":"The energy of a high-frequency photon will be"},{"Start":"05:56.780 ","End":"06:01.235","Text":"much greater than the energy of a low-frequency photon."},{"Start":"06:01.235 ","End":"06:05.915","Text":"If we have many photons we\u0027ll have high intensity."},{"Start":"06:05.915 ","End":"06:09.680","Text":"If we have few photons, we\u0027d have low-intensity."},{"Start":"06:09.680 ","End":"06:11.510","Text":"Let\u0027s take some examples."},{"Start":"06:11.510 ","End":"06:15.820","Text":"Now, X-rays and Gamma rays have very short wavelengths,"},{"Start":"06:15.820 ","End":"06:17.360","Text":"so if they have short wavelengths,"},{"Start":"06:17.360 ","End":"06:19.460","Text":"they have very high frequencies."},{"Start":"06:19.460 ","End":"06:22.205","Text":"Each photon has a high energy."},{"Start":"06:22.205 ","End":"06:28.986","Text":"That\u0027s why they\u0027re so dangerous at high-intensity and can lead to cell mutations."},{"Start":"06:28.986 ","End":"06:31.250","Text":"When they perform X-rays,"},{"Start":"06:31.250 ","End":"06:33.710","Text":"they try to use as little radiation as"},{"Start":"06:33.710 ","End":"06:37.505","Text":"possible in order to limit the number of mutations."},{"Start":"06:37.505 ","End":"06:42.710","Text":"On the other hand, radio waves have very long wavelengths and very low frequencies,"},{"Start":"06:42.710 ","End":"06:45.125","Text":"so each photon has low energy."},{"Start":"06:45.125 ","End":"06:50.540","Text":"We\u0027re surrounded by radio waves so everywhere and they seem to be harmless,"},{"Start":"06:50.540 ","End":"06:52.520","Text":"at least at low intensity."},{"Start":"06:52.520 ","End":"06:55.670","Text":"Some people think they\u0027re harmful at high-intensity,"},{"Start":"06:55.670 ","End":"06:57.335","Text":"but at least at low-intensity,"},{"Start":"06:57.335 ","End":"06:59.600","Text":"they seem to be harmless."},{"Start":"06:59.600 ","End":"07:03.380","Text":"In this video, we talked about black body radiation"},{"Start":"07:03.380 ","End":"07:07.800","Text":"and Planck\u0027s work which lead to quantum mechanics."}],"ID":20867},{"Watched":false,"Name":"Photoelectric Effect","Duration":"4m 40s","ChapterTopicVideoID":20094,"CourseChapterTopicPlaylistID":154567,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20094.jpeg","UploadDate":"2019-11-07T00:29:09.8000000","DurationForVideoObject":"PT4M40S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.740","Text":"In the previous video,"},{"Start":"00:01.740 ","End":"00:04.500","Text":"we talked about the black-body radiation."},{"Start":"00:04.500 ","End":"00:09.945","Text":"In this video, we\u0027ll use the idea of photons to explain the photoelectric effect."},{"Start":"00:09.945 ","End":"00:12.840","Text":"Let\u0027s recall what we learned in the previous video."},{"Start":"00:12.840 ","End":"00:15.075","Text":"We learned about Planck\u0027s equation."},{"Start":"00:15.075 ","End":"00:20.730","Text":"Planck showed that the energy of a photon is proportional to it\u0027s frequency."},{"Start":"00:20.730 ","End":"00:24.300","Text":"The proportionality constant is this h,"},{"Start":"00:24.300 ","End":"00:26.565","Text":"which is called Planck\u0027s constant."},{"Start":"00:26.565 ","End":"00:30.780","Text":"In fact, people used to say that Planck put the h in physics,"},{"Start":"00:30.780 ","End":"00:32.790","Text":"physics is ph,"},{"Start":"00:32.790 ","End":"00:36.755","Text":"that he put the h into the physics."},{"Start":"00:36.755 ","End":"00:39.395","Text":"What\u0027s the photoelectric effect?"},{"Start":"00:39.395 ","End":"00:43.970","Text":"It was discovered by Hertz experimentally in 1888,"},{"Start":"00:43.970 ","End":"00:47.480","Text":"and he got Nobel Prize for it in 1925."},{"Start":"00:47.480 ","End":"00:54.635","Text":"Hertz discovered that when he shone ultraviolet radiation on a metal surface,"},{"Start":"00:54.635 ","End":"00:58.730","Text":"electrons were ejected from the surface."},{"Start":"00:58.730 ","End":"01:01.940","Text":"Now, as you increase the frequency at first,"},{"Start":"01:01.940 ","End":"01:04.340","Text":"no electrons at all are rejected."},{"Start":"01:04.340 ","End":"01:07.130","Text":"It doesn\u0027t matter how intense the radiation is,"},{"Start":"01:07.130 ","End":"01:13.825","Text":"nothing will come out until the frequency of the radiation exceeds a certain threshold,"},{"Start":"01:13.825 ","End":"01:16.990","Text":"and every metal has a different threshold."},{"Start":"01:16.990 ","End":"01:19.850","Text":"It\u0027s a threshold characteristic of the metal."},{"Start":"01:19.850 ","End":"01:23.545","Text":"We\u0027re going to write it as capital Phi,"},{"Start":"01:23.545 ","End":"01:25.755","Text":"it\u0027s called the work function,"},{"Start":"01:25.755 ","End":"01:27.900","Text":"and it\u0027s written capital Phi."},{"Start":"01:27.900 ","End":"01:30.740","Text":"Now, the kinetic energy of these electrons"},{"Start":"01:30.740 ","End":"01:34.040","Text":"is proportional to the frequency of the radiation,"},{"Start":"01:34.040 ","End":"01:37.075","Text":"but independent of the intensity of radiation."},{"Start":"01:37.075 ","End":"01:41.290","Text":"If you can get more and more intense radiation,"},{"Start":"01:41.290 ","End":"01:44.945","Text":"and it won\u0027t change the kinetic energy of the electrons."},{"Start":"01:44.945 ","End":"01:50.450","Text":"Even at very low intensities, electrons are ejected."},{"Start":"01:50.450 ","End":"01:53.105","Text":"What\u0027s the explanation of this phenomenon?"},{"Start":"01:53.105 ","End":"01:59.445","Text":"This was explained by Einstein many years after."},{"Start":"01:59.445 ","End":"02:04.055","Text":"In fact, 17 years after it was discovered by Hertz."},{"Start":"02:04.055 ","End":"02:10.595","Text":"He explained it in 1905 after he knew about what Planck had said."},{"Start":"02:10.595 ","End":"02:13.895","Text":"He got a Nobel Prize for it in 1921."},{"Start":"02:13.895 ","End":"02:16.220","Text":"These were revolutionary discoveries,"},{"Start":"02:16.220 ","End":"02:19.010","Text":"and many people got Nobel Prizes for them."},{"Start":"02:19.010 ","End":"02:21.950","Text":"What Einstein explained was that"},{"Start":"02:21.950 ","End":"02:27.455","Text":"electron is ejected from the metal when a photon of energy,"},{"Start":"02:27.455 ","End":"02:30.835","Text":"E=h Nu, strikes a metal."},{"Start":"02:30.835 ","End":"02:35.200","Text":"He wrote an equation for it, simple equation."},{"Start":"02:35.200 ","End":"02:40.835","Text":"The kinetic energy of an electron is 1/2mv^2."},{"Start":"02:40.835 ","End":"02:42.605","Text":"We\u0027ve seen this many times,"},{"Start":"02:42.605 ","End":"02:44.500","Text":"is equal to h Nu,"},{"Start":"02:44.500 ","End":"02:46.685","Text":"that\u0027s the energy of the photon,"},{"Start":"02:46.685 ","End":"02:50.105","Text":"minus Phi, the work function."},{"Start":"02:50.105 ","End":"02:54.680","Text":"If h Nu is exactly equal to Phi,"},{"Start":"02:54.680 ","End":"02:59.900","Text":"then electron will have no kinetic energy,"},{"Start":"02:59.900 ","End":"03:01.700","Text":"it won\u0027t be ejected at all."},{"Start":"03:01.700 ","End":"03:04.895","Text":"But when h Nu is slightly greater than Phi,"},{"Start":"03:04.895 ","End":"03:10.905","Text":"then we start to have the electron ignited with kinetic energy."},{"Start":"03:10.905 ","End":"03:13.565","Text":"As h Nu gets higher,"},{"Start":"03:13.565 ","End":"03:16.115","Text":"the kinetic energy gets higher."},{"Start":"03:16.115 ","End":"03:19.045","Text":"We can draw a graph of this."},{"Start":"03:19.045 ","End":"03:21.570","Text":"Here we have a graph,"},{"Start":"03:21.570 ","End":"03:24.840","Text":"on the x-axis we have the frequency,"},{"Start":"03:24.840 ","End":"03:28.920","Text":"and on the y-axis we have the kinetic energy."},{"Start":"03:29.390 ","End":"03:32.820","Text":"When the frequency is very low,"},{"Start":"03:32.820 ","End":"03:36.425","Text":"nothing happens, no electrons are emitted."},{"Start":"03:36.425 ","End":"03:40.430","Text":"But then when it gets to exactly equal to Phi,"},{"Start":"03:40.430 ","End":"03:44.915","Text":"over h, then the electrons are emitted."},{"Start":"03:44.915 ","End":"03:48.515","Text":"As Nu, the frequency increases,"},{"Start":"03:48.515 ","End":"03:52.495","Text":"then the kinetic energy increases literally."},{"Start":"03:52.495 ","End":"03:57.260","Text":"This was Einstein\u0027s explanation of the photoelectric effect."},{"Start":"03:57.260 ","End":"04:01.774","Text":"It seems very simple to us now because we\u0027re used to the idea of photons."},{"Start":"04:01.774 ","End":"04:04.525","Text":"But at the time, it was quite revolutionary."},{"Start":"04:04.525 ","End":"04:10.445","Text":"Now, if we want to increase the intensity of the radiation,"},{"Start":"04:10.445 ","End":"04:14.375","Text":"the intensity of the radiation is proportional to the number of photons."},{"Start":"04:14.375 ","End":"04:16.340","Text":"As the intensity increases,"},{"Start":"04:16.340 ","End":"04:18.664","Text":"more electrons are ejected."},{"Start":"04:18.664 ","End":"04:22.880","Text":"In order to increase the kinetic energy,"},{"Start":"04:22.880 ","End":"04:24.845","Text":"you increase the frequency."},{"Start":"04:24.845 ","End":"04:28.115","Text":"In order from more electrons to be emitted,"},{"Start":"04:28.115 ","End":"04:31.925","Text":"you need to increase the intensity of the light."},{"Start":"04:31.925 ","End":"04:35.750","Text":"In this video, we discussed the photoelectric effect,"},{"Start":"04:35.750 ","End":"04:39.480","Text":"and its explanation in terms of photons."}],"ID":20868},{"Watched":false,"Name":"Exercise 1","Duration":"3m 14s","ChapterTopicVideoID":22934,"CourseChapterTopicPlaylistID":154567,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22934.jpeg","UploadDate":"2020-12-16T03:32:30.8930000","DurationForVideoObject":"PT3M14S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.639","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:02.639 ","End":"00:08.475","Text":"What is the energy of radiation of frequency 5.36 times 10^14 inverse seconds?"},{"Start":"00:08.475 ","End":"00:10.920","Text":"A, in joule per photon, b,"},{"Start":"00:10.920 ","End":"00:14.880","Text":"in kilojoule per mole. We\u0027re going to begin with a."},{"Start":"00:14.880 ","End":"00:16.740","Text":"In order to solve this exercise,"},{"Start":"00:16.740 ","End":"00:18.435","Text":"we\u0027re going to use the equation E,"},{"Start":"00:18.435 ","End":"00:20.280","Text":"the energy equals h,"},{"Start":"00:20.280 ","End":"00:22.590","Text":"which is Planck\u0027s constant times nu,"},{"Start":"00:22.590 ","End":"00:24.600","Text":"which is the frequency."},{"Start":"00:24.600 ","End":"00:34.720","Text":"Planck\u0027s constant equals 6.66 times 10 to the negative 34 joules times second."},{"Start":"00:35.570 ","End":"00:40.030","Text":"We\u0027re going to multiply Planck\u0027s constant by the frequency,"},{"Start":"00:40.030 ","End":"00:42.820","Text":"and the frequency is given in that question."},{"Start":"00:42.820 ","End":"00:52.520","Text":"This is times 5.36 times 10^14 inverse seconds."},{"Start":"00:52.520 ","End":"00:55.490","Text":"We can see the second and inverse second cancel out,"},{"Start":"00:55.490 ","End":"00:57.425","Text":"just going to cancel this out."},{"Start":"00:57.425 ","End":"01:07.550","Text":"This equals 3.55 times 10 to the negative 19 joule."},{"Start":"01:07.550 ","End":"01:10.970","Text":"Now, this calculation was actually done for 1 photon,"},{"Start":"01:10.970 ","End":"01:14.640","Text":"and therefore this is joule per photon."},{"Start":"01:15.770 ","End":"01:18.390","Text":"That\u0027s our answer for a."},{"Start":"01:18.390 ","End":"01:24.980","Text":"Again, our answer for a is 3.55 times 10 to the negative 19 joules per photon."},{"Start":"01:24.980 ","End":"01:30.170","Text":"Now we\u0027ll go on to b, and b we want the units in kilojoules per mole."},{"Start":"01:30.170 ","End":"01:34.280","Text":"We\u0027re going to take the energy that we calculated in a,"},{"Start":"01:34.280 ","End":"01:44.040","Text":"which is 3.55 times 10 to the negative 19 joules per photon."},{"Start":"01:45.910 ","End":"01:50.420","Text":"Now again, the energy that we calculated at a is per photon."},{"Start":"01:50.420 ","End":"01:53.720","Text":"Now we want the energy per mole."},{"Start":"01:53.720 ","End":"01:55.280","Text":"The energy per mole,"},{"Start":"01:55.280 ","End":"01:56.960","Text":"just going to write it right here."},{"Start":"01:56.960 ","End":"02:06.655","Text":"The energy per mole equals the energy for 1 photon times Avogadro\u0027s number,"},{"Start":"02:06.655 ","End":"02:09.040","Text":"which is the number of photons in a mole."},{"Start":"02:09.040 ","End":"02:11.290","Text":"We\u0027re going to take the energy from a,"},{"Start":"02:11.290 ","End":"02:14.965","Text":"3.55 times 10 to the negative 19 joules per photon,"},{"Start":"02:14.965 ","End":"02:19.180","Text":"and multiply this by Avogadro\u0027s number,"},{"Start":"02:19.180 ","End":"02:25.960","Text":"which is 6.022 times 10^23,"},{"Start":"02:25.960 ","End":"02:28.700","Text":"and this is photons in 1 mole."},{"Start":"02:30.240 ","End":"02:33.250","Text":"Then the photons cancel out."},{"Start":"02:33.250 ","End":"02:36.710","Text":"Now we also want kilojoules in our units instead of joules."},{"Start":"02:36.710 ","End":"02:39.355","Text":"We\u0027re going to multiply this by a conversion factor."},{"Start":"02:39.355 ","End":"02:47.970","Text":"We\u0027re going to multiply this by 1 kilojoule per 1,000 joules,"},{"Start":"02:47.970 ","End":"02:51.450","Text":"because we have 1,000 joules in 1 kilojoule."},{"Start":"02:51.450 ","End":"02:54.400","Text":"The joules are going to cancel out,"},{"Start":"02:54.400 ","End":"02:57.950","Text":"and we\u0027ll be left with kilojoules per mole."},{"Start":"02:57.950 ","End":"03:05.550","Text":"This comes to 213.78 kilojoules per mole."},{"Start":"03:05.830 ","End":"03:11.810","Text":"That\u0027s our answer for b. These are our final answers."},{"Start":"03:11.810 ","End":"03:14.460","Text":"Thank you very much for watching."}],"ID":23755},{"Watched":false,"Name":"Exercise 2","Duration":"3m 49s","ChapterTopicVideoID":22935,"CourseChapterTopicPlaylistID":154567,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22935.jpeg","UploadDate":"2020-12-16T03:32:40.7700000","DurationForVideoObject":"PT3M49S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.220","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:03.220 ","End":"00:08.920","Text":"Determine the energy of radiation with a wavelength of 470 nanometers: a,"},{"Start":"00:08.920 ","End":"00:10.314","Text":"in joule per photon;"},{"Start":"00:10.314 ","End":"00:11.980","Text":"b, in joule per mole."},{"Start":"00:11.980 ","End":"00:16.615","Text":"We have to find the energy in this question and we know the wavelength."},{"Start":"00:16.615 ","End":"00:18.130","Text":"We\u0027re going to use two equations here."},{"Start":"00:18.130 ","End":"00:21.100","Text":"One is E, the energy equals h,"},{"Start":"00:21.100 ","End":"00:22.930","Text":"which is Planck\u0027s constant times nu,"},{"Start":"00:22.930 ","End":"00:25.365","Text":"which is the frequency."},{"Start":"00:25.365 ","End":"00:28.125","Text":"The second equation is c,"},{"Start":"00:28.125 ","End":"00:32.580","Text":"which is the speed of light constant equals Lambda,"},{"Start":"00:32.580 ","End":"00:35.010","Text":"which is the wavelength times nu,"},{"Start":"00:35.010 ","End":"00:36.555","Text":"which is the frequency."},{"Start":"00:36.555 ","End":"00:39.355","Text":"Now, if we divide both sides by lambda,"},{"Start":"00:39.355 ","End":"00:41.170","Text":"we\u0027re going to get nu,"},{"Start":"00:41.170 ","End":"00:45.395","Text":"which is the frequency equals c divided by Lambda."},{"Start":"00:45.395 ","End":"00:50.600","Text":"Now, we\u0027re going to combine this equation and our first equation."},{"Start":"00:50.600 ","End":"00:57.330","Text":"E equals h nu,"},{"Start":"00:57.330 ","End":"01:01.110","Text":"which equals hc divided by Lambda."},{"Start":"01:01.110 ","End":"01:02.975","Text":"We\u0027ll just write that right here again,"},{"Start":"01:02.975 ","End":"01:09.365","Text":"E equals hc divided by lambda and h is Planck\u0027s constant and"},{"Start":"01:09.365 ","End":"01:17.550","Text":"equals 6.626 times 10 to the negative 34 joules times second."},{"Start":"01:17.550 ","End":"01:19.730","Text":"We\u0027re going to multiply it by c,"},{"Start":"01:19.730 ","End":"01:21.440","Text":"which is the speed of light."},{"Start":"01:21.440 ","End":"01:27.960","Text":"This is rounded off to 3 times 10^8 meters per second."},{"Start":"01:28.760 ","End":"01:32.410","Text":"All of this is divided by Lambda,"},{"Start":"01:32.410 ","End":"01:34.690","Text":"which is the wavelength, and this is given,"},{"Start":"01:34.690 ","End":"01:37.970","Text":"it equals 470 nanometers."},{"Start":"01:40.730 ","End":"01:45.400","Text":"Now, first of all, we can see that the seconds cancel out because we"},{"Start":"01:45.400 ","End":"01:49.705","Text":"have second divided by second and we\u0027re left with joule times meter."},{"Start":"01:49.705 ","End":"01:52.180","Text":"Here in the denominator we have nanometers."},{"Start":"01:52.180 ","End":"01:54.875","Text":"We\u0027re going to multiply by a conversion factor"},{"Start":"01:54.875 ","End":"01:58.850","Text":"in order to convert the nanometers to meters."},{"Start":"02:00.710 ","End":"02:08.432","Text":"This is the same as 1 meter per 10^9 nanometers."},{"Start":"02:08.432 ","End":"02:12.720","Text":"The nanometers cancel out and the meters also cancel out."},{"Start":"02:12.720 ","End":"02:21.210","Text":"This equals 4.23 times 10 to the negative 19."},{"Start":"02:21.210 ","End":"02:24.510","Text":"This is joules."},{"Start":"02:24.510 ","End":"02:27.850","Text":"The calculation that we did here is for 1 photon,"},{"Start":"02:27.850 ","End":"02:30.270","Text":"therefore it\u0027s joules per photon."},{"Start":"02:31.270 ","End":"02:33.410","Text":"That\u0027s our answer for a,"},{"Start":"02:33.410 ","End":"02:37.300","Text":"4.23 times 10 to the negative 19 joule per photon."},{"Start":"02:37.300 ","End":"02:39.120","Text":"Now, we\u0027re going on to b and in b,"},{"Start":"02:39.120 ","End":"02:42.235","Text":"we want our units to be joule per mole."},{"Start":"02:42.235 ","End":"02:46.810","Text":"Again, in a, we found that the energy equals 4.23"},{"Start":"02:46.810 ","End":"02:52.620","Text":"times 10 to the negative 19 joule per photon."},{"Start":"02:52.780 ","End":"02:57.770","Text":"We want to convert the joule per photon to joule per mole."},{"Start":"02:57.770 ","End":"03:03.750","Text":"The energy of a mole equals the energy of"},{"Start":"03:03.750 ","End":"03:08.115","Text":"a photon times Avogadro\u0027s number"},{"Start":"03:08.115 ","End":"03:12.080","Text":"since Avogadro\u0027s number is the number of photons in 1 mole."},{"Start":"03:12.080 ","End":"03:14.810","Text":"We\u0027re going to take the energy that we found an a,"},{"Start":"03:14.810 ","End":"03:17.570","Text":"we\u0027re going to multiply this by Avogadro\u0027s numbers,"},{"Start":"03:17.570 ","End":"03:21.770","Text":"so we\u0027re going to multiply this by 6.022 times 10^23 photons per mole."},{"Start":"03:21.770 ","End":"03:30.840","Text":"The photons are going to"},{"Start":"03:30.840 ","End":"03:41.200","Text":"cancel out and this equals 254730.6 joule per mole."},{"Start":"03:42.230 ","End":"03:45.580","Text":"That is our answer for b."},{"Start":"03:46.430 ","End":"03:49.960","Text":"Thank you very much for watching."}],"ID":23756},{"Watched":false,"Name":"Exercise 3","Duration":"3m 34s","ChapterTopicVideoID":22936,"CourseChapterTopicPlaylistID":154567,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22936.jpeg","UploadDate":"2020-12-16T03:32:50.2570000","DurationForVideoObject":"PT3M34S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.435","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:03.435 ","End":"00:09.240","Text":"Arrange the following wavelengths in order of increasing energy: A, 7.82 micrometers;"},{"Start":"00:09.240 ","End":"00:11.550","Text":"B, 322 nanometers; C,"},{"Start":"00:11.550 ","End":"00:14.895","Text":"6.35 times 10^-5 centimeters."},{"Start":"00:14.895 ","End":"00:16.695","Text":"The first step we\u0027re going to do,"},{"Start":"00:16.695 ","End":"00:20.940","Text":"is to convert all of these wavelengths into the same units."},{"Start":"00:20.940 ","End":"00:22.380","Text":"We\u0027re going to convert it all into meters."},{"Start":"00:22.380 ","End":"00:27.910","Text":"If we look at A, we have 7.82 micrometers."},{"Start":"00:27.910 ","End":"00:30.110","Text":"We\u0027re going to multiply this by a conversion factor."},{"Start":"00:30.110 ","End":"00:34.130","Text":"In every 1 meter, we have 10^6 micrometers."},{"Start":"00:34.130 ","End":"00:35.645","Text":"The micrometers cancel out,"},{"Start":"00:35.645 ","End":"00:42.450","Text":"and this equals 7.82 times 10^-6 meters."},{"Start":"00:42.450 ","End":"00:43.710","Text":"Next, we\u0027ll go onto B."},{"Start":"00:43.710 ","End":"00:47.260","Text":"We have 322 nanometers."},{"Start":"00:48.460 ","End":"00:51.770","Text":"Again, we\u0027re going to multiply this by a conversion factor."},{"Start":"00:51.770 ","End":"00:56.105","Text":"In every 1 meter, we have 10^9 nanometers."},{"Start":"00:56.105 ","End":"00:57.890","Text":"Nanometers will cancel out,"},{"Start":"00:57.890 ","End":"01:05.555","Text":"and this equals 322 times 10^-9 meters."},{"Start":"01:05.555 ","End":"01:12.605","Text":"This equals 3.22 times 10^-7 meters."},{"Start":"01:12.605 ","End":"01:18.510","Text":"In C, we have 6.35 times 10^-5 centimeters."},{"Start":"01:23.860 ","End":"01:29.570","Text":"We\u0027re going to multiply this by 1 meter per 100 centimeters."},{"Start":"01:29.570 ","End":"01:31.790","Text":"The centimeters cancel out,"},{"Start":"01:31.790 ","End":"01:39.565","Text":"and this equals 6.35 times 10^-7 meters."},{"Start":"01:39.565 ","End":"01:42.410","Text":"Now if we compare wavelengths, we can see that in A,"},{"Start":"01:42.410 ","End":"01:45.510","Text":"we have the largest wavelength,"},{"Start":"01:46.120 ","End":"01:49.700","Text":"then we go on to C,"},{"Start":"01:49.700 ","End":"01:52.975","Text":"6.35 times 10^-7 meters,"},{"Start":"01:52.975 ","End":"01:57.540","Text":"and B is the lowest wavelength,"},{"Start":"01:57.540 ","End":"02:01.575","Text":"or the smallest wavelength, 3.22 times 10^-7 meters."},{"Start":"02:01.575 ","End":"02:06.020","Text":"Now, we\u0027re asked to arrange the following wavelengths in order of increasing energy."},{"Start":"02:06.020 ","End":"02:14.010","Text":"The equation that compares between energy and wavelength is E=h nu."},{"Start":"02:14.010 ","End":"02:17.085","Text":"This equals hc divided by Lambda."},{"Start":"02:17.085 ","End":"02:24.420","Text":"Again, we\u0027re just going to write, E equals hc divided by Lambda."},{"Start":"02:24.420 ","End":"02:30.530","Text":"We can see that if we want the energy to increase,"},{"Start":"02:30.530 ","End":"02:33.830","Text":"we need the wavelengths to decrease in size,"},{"Start":"02:33.830 ","End":"02:36.790","Text":"since we have Lambda in the denominator."},{"Start":"02:36.790 ","End":"02:40.730","Text":"Again, we know that the largest wavelength is in A."},{"Start":"02:40.730 ","End":"02:44.945","Text":"Then we have C, and then we have B, the smallest wavelength."},{"Start":"02:44.945 ","End":"02:47.450","Text":"The largest wavelength, which is a,"},{"Start":"02:47.450 ","End":"02:50.675","Text":"is going to give us the lowest energy."},{"Start":"02:50.675 ","End":"02:53.405","Text":"Again, since Lambda is in the denominator."},{"Start":"02:53.405 ","End":"02:56.290","Text":"The lowest energy is going to be A."},{"Start":"02:56.290 ","End":"02:58.605","Text":"Next we have C,"},{"Start":"02:58.605 ","End":"03:00.870","Text":"which is smaller than A."},{"Start":"03:00.870 ","End":"03:03.675","Text":"The energy will increase."},{"Start":"03:03.675 ","End":"03:05.840","Text":"Last we have B,"},{"Start":"03:05.840 ","End":"03:07.835","Text":"which is the smallest of the wavelength."},{"Start":"03:07.835 ","End":"03:11.000","Text":"Therefore, the energy is going to be the largest."},{"Start":"03:11.000 ","End":"03:13.310","Text":"In order of increasing energy,"},{"Start":"03:13.310 ","End":"03:15.470","Text":"we have A which has the lowest energy,"},{"Start":"03:15.470 ","End":"03:17.285","Text":"and remember largest wavelength."},{"Start":"03:17.285 ","End":"03:19.765","Text":"Then we have C, which is in the middle in both."},{"Start":"03:19.765 ","End":"03:22.520","Text":"Then B, which is the smallest wavelength,"},{"Start":"03:22.520 ","End":"03:25.100","Text":"gives us the largest energy."},{"Start":"03:25.100 ","End":"03:27.245","Text":"Our answer is A,"},{"Start":"03:27.245 ","End":"03:29.600","Text":"is smaller than C, is smaller than B."},{"Start":"03:29.600 ","End":"03:31.370","Text":"That is our final answer."},{"Start":"03:31.370 ","End":"03:34.260","Text":"Thank you very much for watching."}],"ID":23757}],"Thumbnail":null,"ID":154567},{"Name":"Bohr Model of Hydrogen Atom","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Bohr Model of the Hydrogen Atom","Duration":"7m 22s","ChapterTopicVideoID":20157,"CourseChapterTopicPlaylistID":154568,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20157.jpeg","UploadDate":"2019-07-10T23:12:20.1930000","DurationForVideoObject":"PT7M22S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.265","Text":"In the previous video,"},{"Start":"00:02.265 ","End":"00:08.700","Text":"we saw that the emission spectrum of hydrogen consists of only 4 lines in the visible."},{"Start":"00:08.700 ","End":"00:12.195","Text":"In this video, we\u0027ll talk about the Bohr model,"},{"Start":"00:12.195 ","End":"00:15.490","Text":"which explains why this is so."},{"Start":"00:23.240 ","End":"00:28.440","Text":"Let\u0027s first talk about the failure of the classical theory."},{"Start":"00:29.590 ","End":"00:32.300","Text":"According to classical theory,"},{"Start":"00:32.300 ","End":"00:35.240","Text":"if the negatively charged electrons"},{"Start":"00:35.240 ","End":"00:38.830","Text":"are moving around the central positively charged nucleus,"},{"Start":"00:38.830 ","End":"00:41.780","Text":"they should accelerate and lose energy,"},{"Start":"00:41.780 ","End":"00:45.590","Text":"eventually spiraling into the nucleus."},{"Start":"00:45.590 ","End":"00:48.860","Text":"Here\u0027s our nucleus positively-charged."},{"Start":"00:48.860 ","End":"00:51.725","Text":"Here\u0027s our electron negatively charged."},{"Start":"00:51.725 ","End":"00:53.220","Text":"As it goes round,"},{"Start":"00:53.220 ","End":"01:00.030","Text":"it eventually spirals into the nucleus, destroying the atom."},{"Start":"01:03.680 ","End":"01:06.045","Text":"This is clearly wrong,"},{"Start":"01:06.045 ","End":"01:10.140","Text":"as we know that hydrogen atoms are stable."},{"Start":"01:15.730 ","End":"01:19.055","Text":"Now we\u0027re going to describe the Bohr atom."},{"Start":"01:19.055 ","End":"01:23.840","Text":"The description given by Niels Bohr in 1913,"},{"Start":"01:23.840 ","End":"01:27.900","Text":"for which he won the Nobel Prize in 1922."},{"Start":"01:29.750 ","End":"01:34.425","Text":"Niels Bohr used Planck\u0027s hypothesis;"},{"Start":"01:34.425 ","End":"01:37.580","Text":"the energy is quantized together with"},{"Start":"01:37.580 ","End":"01:42.780","Text":"some classical physics to construct a model of a hydrogen atom."},{"Start":"01:46.580 ","End":"01:53.545","Text":"He said that the electron moves in 1 of a set of circular orbits around the nucleus,"},{"Start":"01:53.545 ","End":"02:00.005","Text":"and each orbit has a fixed radius and a fixed energy."},{"Start":"02:00.005 ","End":"02:07.045","Text":"Here\u0027s our nucleus, and the electron is moving around it in a fixed orbit."},{"Start":"02:07.045 ","End":"02:10.520","Text":"Circle is electron."},{"Start":"02:10.520 ","End":"02:13.475","Text":"The first one is n=1."},{"Start":"02:13.475 ","End":"02:15.995","Text":"That\u0027s the quantum number, n=1."},{"Start":"02:15.995 ","End":"02:21.020","Text":"Whereas, the second one is n=2 and so on."},{"Start":"02:23.030 ","End":"02:25.375","Text":"If the electron is 2,"},{"Start":"02:25.375 ","End":"02:28.865","Text":"it can emit energy and go down to 1."},{"Start":"02:28.865 ","End":"02:31.685","Text":"Whereas, if the energy is n=1,"},{"Start":"02:31.685 ","End":"02:36.590","Text":"it can absorb energy and go up to n=2."},{"Start":"02:36.790 ","End":"02:44.760","Text":"Energy is only emitted or absorbed when electron moves to a lower or higher orbit."},{"Start":"02:45.880 ","End":"02:50.880","Text":"Now what are the radii of these allowed orbits?"},{"Start":"02:54.980 ","End":"03:01.140","Text":"The radius of the nth orbit is n^2 a_0,"},{"Start":"03:01.140 ","End":"03:04.335","Text":"where n can be 1,2,3 and so on,"},{"Start":"03:04.335 ","End":"03:10.220","Text":"and a_0 is called the Bohr radius and has a value of 0.0529"},{"Start":"03:10.220 ","End":"03:17.995","Text":"nanometers or 52.9 picometers, whichever you prefer."},{"Start":"03:17.995 ","End":"03:22.860","Text":"The lowest orbit is r_1 and that has"},{"Start":"03:22.860 ","End":"03:30.987","Text":"a radius a_0 and the r_2 has a radius of 4a_0."},{"Start":"03:30.987 ","End":"03:38.096","Text":"Now, n equal to 1,2,3, etc."},{"Start":"03:38.096 ","End":"03:41.255","Text":"are called the quantum numbers,"},{"Start":"03:41.255 ","End":"03:42.950","Text":"as we said before a_0,"},{"Start":"03:42.950 ","End":"03:45.780","Text":"is called the Bohr radius."},{"Start":"03:46.270 ","End":"03:51.030","Text":"Now what are the energies of these levels?"},{"Start":"03:54.740 ","End":"04:01.840","Text":"According to Bohr, the energy of the nth level is equal to minus R_H,"},{"Start":"04:01.840 ","End":"04:05.530","Text":"which is a constant, divided by n^2."},{"Start":"04:05.530 ","End":"04:10.990","Text":"R_H is equal to 2.179 times 10^-18 joules,"},{"Start":"04:10.990 ","End":"04:13.885","Text":"and it\u0027s called the Rydberg constant."},{"Start":"04:13.885 ","End":"04:16.975","Text":"You see that all the energies are negative."},{"Start":"04:16.975 ","End":"04:20.425","Text":"The most negative one is the most stable."},{"Start":"04:20.425 ","End":"04:23.570","Text":"That\u0027s with n equal to 1."},{"Start":"04:25.830 ","End":"04:28.780","Text":"The lowest energy level,"},{"Start":"04:28.780 ","End":"04:30.745","Text":"which we call the ground state,"},{"Start":"04:30.745 ","End":"04:37.220","Text":"has n equal to 1 and its energy is E_1 equal to minus R_H."},{"Start":"04:38.180 ","End":"04:41.872","Text":"Then we have the excited states with n equal to 2,"},{"Start":"04:41.872 ","End":"04:44.240","Text":"3, 4 and so on."},{"Start":"04:45.060 ","End":"04:52.480","Text":"Until we get to the highest level or highest levels where n is equal to"},{"Start":"04:52.480 ","End":"04:59.380","Text":"infinity and e infinity is equal to 0 because we\u0027re dividing by infinity,"},{"Start":"04:59.380 ","End":"05:01.615","Text":"divided by infinity, we get 0."},{"Start":"05:01.615 ","End":"05:03.625","Text":"Now that\u0027s the highest level,"},{"Start":"05:03.625 ","End":"05:06.025","Text":"that\u0027s when ionization occurs."},{"Start":"05:06.025 ","End":"05:10.405","Text":"The electron is completely disconnected from the nucleus."},{"Start":"05:10.405 ","End":"05:13.120","Text":"We have the nucleus and the electron far,"},{"Start":"05:13.120 ","End":"05:16.910","Text":"far away, no relation between them."},{"Start":"05:18.710 ","End":"05:21.820","Text":"Now, we can draw this."},{"Start":"05:23.230 ","End":"05:27.595","Text":"We have, here\u0027s the lowest n=1,"},{"Start":"05:27.595 ","End":"05:32.103","Text":"n=2, n=3, 4, 5,"},{"Start":"05:32.103 ","End":"05:40.050","Text":"6, then"},{"Start":"05:40.050 ","End":"05:43.120","Text":"n equal to infinity."},{"Start":"05:43.830 ","End":"05:48.610","Text":"Now we can explain the spectra we saw before."},{"Start":"05:48.610 ","End":"05:53.274","Text":"Here is n=1, 2,"},{"Start":"05:53.274 ","End":"05:55.443","Text":"3, 4,"},{"Start":"05:55.443 ","End":"05:59.030","Text":"5, 6 and infinity."},{"Start":"06:01.280 ","End":"06:10.235","Text":"What we see in the visible spectrum are all the emission spectra that end up in n=2."},{"Start":"06:10.235 ","End":"06:12.305","Text":"We have 3-2,"},{"Start":"06:12.305 ","End":"06:17.380","Text":"4-2, 5-2, and 6-2."},{"Start":"06:17.380 ","End":"06:20.330","Text":"That\u0027s the four lines that we see in"},{"Start":"06:20.330 ","End":"06:25.160","Text":"the emission spectra of hydrogen in the visible region."},{"Start":"06:25.160 ","End":"06:28.620","Text":"That\u0027s called the Balmer series."},{"Start":"06:29.410 ","End":"06:33.760","Text":"Then, we have a series ends up in n=1."},{"Start":"06:33.760 ","End":"06:39.000","Text":"That\u0027s n=2-1, 3-1,"},{"Start":"06:39.000 ","End":"06:41.205","Text":"4-1 and so on."},{"Start":"06:41.205 ","End":"06:45.940","Text":"That\u0027s in the ultraviolet and it\u0027s called the Lyman series."},{"Start":"06:45.940 ","End":"06:48.350","Text":"Then there are many other series,"},{"Start":"06:48.350 ","End":"06:52.295","Text":"but the next one we\u0027ll talk about is 4-3,"},{"Start":"06:52.295 ","End":"06:54.800","Text":"5-3 and so on."},{"Start":"06:54.800 ","End":"06:57.620","Text":"That\u0027s called the Paschen series."},{"Start":"06:57.620 ","End":"07:00.530","Text":"That appears in the infrared."},{"Start":"07:00.530 ","End":"07:04.670","Text":"Because you see the energy differences are much smaller than in the"},{"Start":"07:04.670 ","End":"07:09.995","Text":"visible and they are in turn much smaller than in the ultraviolet."},{"Start":"07:09.995 ","End":"07:13.250","Text":"In this video, we\u0027ve started the discussion of"},{"Start":"07:13.250 ","End":"07:17.910","Text":"the Bohr atom and we\u0027ll continue it in the next video."}],"ID":23758},{"Watched":false,"Name":"Spectra of Hydrogen Atom","Duration":"8m 20s","ChapterTopicVideoID":20156,"CourseChapterTopicPlaylistID":154568,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20156.jpeg","UploadDate":"2019-07-10T23:10:56.0200000","DurationForVideoObject":"PT8M20S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.605","Text":"In the previous video,"},{"Start":"00:01.605 ","End":"00:04.620","Text":"we introduced the Bohr model of the hydrogen atom."},{"Start":"00:04.620 ","End":"00:09.405","Text":"In this video, we\u0027ll talk about the spectrum of the hydrogen atom."},{"Start":"00:09.405 ","End":"00:12.165","Text":"Let\u0027s begin with emission spectrum."},{"Start":"00:12.165 ","End":"00:20.025","Text":"If we heat a hydrogen atom or excited in some other way such as electrical discharge,"},{"Start":"00:20.025 ","End":"00:22.775","Text":"electrons will be excited to higher levels."},{"Start":"00:22.775 ","End":"00:26.855","Text":"They then emits radiation and return to a lower level."},{"Start":"00:26.855 ","End":"00:28.385","Text":"Let\u0027s illustrate this."},{"Start":"00:28.385 ","End":"00:31.700","Text":"Here\u0027s our lower level and our excited level."},{"Start":"00:31.700 ","End":"00:34.345","Text":"I\u0027m going to call the lower-level E_1,"},{"Start":"00:34.345 ","End":"00:37.315","Text":"and the excited level E_2."},{"Start":"00:37.315 ","End":"00:42.625","Text":"Now, if we excite an atom from E_1 to E_2,"},{"Start":"00:42.625 ","End":"00:44.180","Text":"it won\u0027t stay there."},{"Start":"00:44.180 ","End":"00:49.850","Text":"The electron will emit radiation and return to E_1."},{"Start":"00:49.850 ","End":"00:52.715","Text":"Here it will emit radiation."},{"Start":"00:52.715 ","End":"00:57.300","Text":"This radiation is called spontaneous emission."},{"Start":"01:03.650 ","End":"01:08.200","Text":"Now the difference in energy between E_2 and E_1 is"},{"Start":"01:08.200 ","End":"01:14.995","Text":"Delta E. In order to get the frequency of the light emitted,"},{"Start":"01:14.995 ","End":"01:19.780","Text":"that will we have to write Delta E is equal to h nu."},{"Start":"01:19.780 ","End":"01:22.330","Text":"Once we\u0027ll calculate a Delta E,"},{"Start":"01:22.330 ","End":"01:24.535","Text":"we can calculate the frequency."},{"Start":"01:24.535 ","End":"01:29.155","Text":"If we want, we can go from the frequency to the wavelength."},{"Start":"01:29.155 ","End":"01:35.665","Text":"Here\u0027s our expression taken from the Bohr expression for the energy levels."},{"Start":"01:35.665 ","End":"01:38.880","Text":"Delta E is equal to E_2 minus E_1."},{"Start":"01:38.880 ","End":"01:45.600","Text":"We know from Bohr the E_2 is minus R_H times 1 over n_2_2,"},{"Start":"01:45.600 ","End":"01:51.015","Text":"and E_1 is minus R_H times 1 over n_1_2."},{"Start":"01:51.015 ","End":"01:53.295","Text":"We\u0027ve written all together here."},{"Start":"01:53.295 ","End":"02:02.665","Text":"Delta E is minus R_H Rydberg constant times in (1_2^2 minus 1_1^2)."},{"Start":"02:02.665 ","End":"02:07.310","Text":"Now, we can change the sign of that and write R_H and then change"},{"Start":"02:07.310 ","End":"02:12.785","Text":"the order in the brackets times 1 over n_1 ^2 minus 1 over n_2^2."},{"Start":"02:12.785 ","End":"02:21.170","Text":"We know the value of the Rydberg constant is 2.179 times 10_minus 18 joules."},{"Start":"02:21.170 ","End":"02:30.255","Text":"Now, we have the expression for Delta E. This is the expression for Delta E. Now,"},{"Start":"02:30.255 ","End":"02:31.930","Text":"in order to get the frequency,"},{"Start":"02:31.930 ","End":"02:37.416","Text":"we have to divide by h. Here\u0027s expression we had for Delta E,"},{"Start":"02:37.416 ","End":"02:45.305","Text":"2.179 times 10_minus 18 joules times 1 over n_1^2 minus 1 over n_2^2."},{"Start":"02:45.305 ","End":"02:47.620","Text":"We\u0027re going to divide by h. Now,"},{"Start":"02:47.620 ","End":"02:55.150","Text":"we can put in the numbers 2.179 times 10_minus 18 joules divided by the value of h,"},{"Start":"02:55.150 ","End":"03:02.020","Text":"which is 6.626 times 10_minus 34 joules times seconds."},{"Start":"03:02.020 ","End":"03:05.319","Text":"Then we have the same expression as before in the brackets."},{"Start":"03:05.319 ","End":"03:07.510","Text":"The joules cancels."},{"Start":"03:07.510 ","End":"03:10.194","Text":"We\u0027re left with 1 over second."},{"Start":"03:10.194 ","End":"03:16.400","Text":"We know that second to the minus 1 is the same as hertz."},{"Start":"03:16.400 ","End":"03:24.440","Text":"Our expression once we\u0027ve divided is 3.288 times 10_15 times 1 over n,"},{"Start":"03:24.440 ","End":"03:28.170","Text":"1^2 minus 1 over n_2^2."},{"Start":"03:29.410 ","End":"03:33.545","Text":"That\u0027s our expression for the frequency."},{"Start":"03:33.545 ","End":"03:38.150","Text":"Now in a previous video code, atomic spectra,"},{"Start":"03:38.150 ","End":"03:44.040","Text":"we inserted the numbers for n_1 and n_2."},{"Start":"03:44.040 ","End":"03:47.770","Text":"We did n_1 is equal to 2,"},{"Start":"03:49.730 ","End":"03:53.055","Text":"n_2 equals to 3."},{"Start":"03:53.055 ","End":"03:56.750","Text":"We saw that we\u0027ve got the color red."},{"Start":"03:56.750 ","End":"04:00.150","Text":"That was red light that was emitted."},{"Start":"04:01.240 ","End":"04:06.110","Text":"That red light is part of the Balmer series."},{"Start":"04:06.110 ","End":"04:11.965","Text":"The Balmer series always ends up in n_1 equal to 2."},{"Start":"04:11.965 ","End":"04:16.920","Text":"This is 2. Then we get transitions from 3 to 2."},{"Start":"04:16.920 ","End":"04:20.198","Text":"We saw that was red,"},{"Start":"04:20.198 ","End":"04:22.002","Text":"from 4 to 2,"},{"Start":"04:22.002 ","End":"04:27.805","Text":"then for 5 to 2 and 6 to 2,"},{"Start":"04:27.805 ","End":"04:31.400","Text":"this is a bluey-green and this is purple and purple."},{"Start":"04:31.400 ","End":"04:38.310","Text":"We get in fact four lines in the emission spectrum of hydrogen."},{"Start":"04:38.450 ","End":"04:43.685","Text":"Now there are series, this alignment series which is not in the visible."},{"Start":"04:43.685 ","End":"04:46.500","Text":"Here, we\u0027re ending up in n_1 equal to 1,"},{"Start":"04:46.500 ","End":"04:48.145","Text":"so this is now 1."},{"Start":"04:48.145 ","End":"04:51.700","Text":"That\u0027s in the UV,"},{"Start":"04:51.700 ","End":"04:55.310","Text":"or the Paschen series where the lower level is 3,"},{"Start":"04:55.310 ","End":"04:58.400","Text":"and that gives us infrared radiation."},{"Start":"04:58.400 ","End":"05:05.640","Text":"Now, if we take the red light that\u0027s emitted from 3 to 2,"},{"Start":"05:05.640 ","End":"05:07.170","Text":"and now we take a laser,"},{"Start":"05:07.170 ","End":"05:08.779","Text":"say a red laser."},{"Start":"05:08.779 ","End":"05:12.427","Text":"Often precisely the same frequencies was emitted,"},{"Start":"05:12.427 ","End":"05:16.430","Text":"we can excite the atom from 2 to 3."},{"Start":"05:16.430 ","End":"05:19.985","Text":"Here\u0027s our lower-level our upper level,"},{"Start":"05:19.985 ","End":"05:23.465","Text":"our lower level is n_1 equal to 2."},{"Start":"05:23.465 ","End":"05:26.675","Text":"We want to get to n_2 equal to 3."},{"Start":"05:26.675 ","End":"05:31.940","Text":"We take the red light and we shine it on the atom,"},{"Start":"05:31.940 ","End":"05:34.190","Text":"and we\u0027ll go from 2 to 3."},{"Start":"05:34.190 ","End":"05:38.000","Text":"Now supposing the lower level is 1,"},{"Start":"05:38.000 ","End":"05:39.530","Text":"that\u0027s the ground state,"},{"Start":"05:39.530 ","End":"05:41.300","Text":"the lowest possible level."},{"Start":"05:41.300 ","End":"05:44.040","Text":"We want to go to the highest possible level,"},{"Start":"05:44.040 ","End":"05:47.010","Text":"that\u0027s n_2 is equal to infinity."},{"Start":"05:47.010 ","End":"05:52.455","Text":"We want to go from n_1 to n_2."},{"Start":"05:52.455 ","End":"05:58.215","Text":"N_1 is 1 the ground level and n_2 is infinity."},{"Start":"05:58.215 ","End":"06:04.201","Text":"This is called ionization"},{"Start":"06:04.201 ","End":"06:09.500","Text":"because when n is very large,"},{"Start":"06:09.500 ","End":"06:14.525","Text":"the electron is completely dissociated from the nucleus."},{"Start":"06:14.525 ","End":"06:18.950","Text":"In fact, the electron doesn\u0027t belong to that nucleus anymore."},{"Start":"06:18.950 ","End":"06:24.085","Text":"We\u0027ve gone from H to H plus,"},{"Start":"06:24.085 ","End":"06:26.915","Text":"we\u0027ve ionized the hydrogen atom."},{"Start":"06:26.915 ","End":"06:30.905","Text":"What energy do we require for this?"},{"Start":"06:30.905 ","End":"06:35.585","Text":"Now, Delta E is equal to 2.179 times"},{"Start":"06:35.585 ","End":"06:42.315","Text":"10^minus 18 joules times 1 over n_1^2 minus 1 over n_2^2."},{"Start":"06:42.315 ","End":"06:43.680","Text":"N_1 is 1,"},{"Start":"06:43.680 ","End":"06:44.900","Text":"so this is just 1,"},{"Start":"06:44.900 ","End":"06:48.120","Text":"1 over infinity is 0,"},{"Start":"06:48.120 ","End":"06:50.085","Text":"so we\u0027re just left with 1."},{"Start":"06:50.085 ","End":"06:58.010","Text":"The answer is Delta E is equal to 2.179 times 10^minus 18 joules."},{"Start":"06:58.010 ","End":"07:04.150","Text":"Now, this is the ionization energy just for 1 single atom."},{"Start":"07:04.150 ","End":"07:07.075","Text":"This is for 1 atom."},{"Start":"07:07.075 ","End":"07:09.590","Text":"Now, later on,"},{"Start":"07:09.590 ","End":"07:14.660","Text":"we will talk about ionization energies of atoms."},{"Start":"07:14.660 ","End":"07:17.210","Text":"This is I_1 in this case because there\u0027s"},{"Start":"07:17.210 ","End":"07:20.995","Text":"only one possibility for hydrogen has only one electron."},{"Start":"07:20.995 ","End":"07:28.610","Text":"We want to calculate how much energy is required to ionize a whole mole of atoms,"},{"Start":"07:28.610 ","End":"07:29.915","Text":"not just a single atom,"},{"Start":"07:29.915 ","End":"07:31.250","Text":"but a whole mole."},{"Start":"07:31.250 ","End":"07:37.070","Text":"Here\u0027s the answer. I_1 is usually called I_1 is equal to this Delta E that we had before,"},{"Start":"07:37.070 ","End":"07:41.600","Text":"2.179 times 10 to the minus 18 joules per atom."},{"Start":"07:41.600 ","End":"07:43.610","Text":"But we want for a whole mole,"},{"Start":"07:43.610 ","End":"07:47.210","Text":"so we have to multiply by Avogadro\u0027s number,"},{"Start":"07:47.210 ","End":"07:52.790","Text":"6.022 times 10^23 atoms per mole,"},{"Start":"07:52.790 ","End":"07:59.180","Text":"and then we get atoms per minus 1 times atoms is just 1 and we\u0027re left per mole."},{"Start":"07:59.180 ","End":"08:00.680","Text":"We multiply all that out,"},{"Start":"08:00.680 ","End":"08:05.285","Text":"we get 1312 kilojoules per mole."},{"Start":"08:05.285 ","End":"08:12.770","Text":"That\u0027s the energy required to ionize a whole mole of hydrogen atoms."},{"Start":"08:12.770 ","End":"08:20.520","Text":"In this video, we discussed the emission and absorption spectra of hydrogen atom."}],"ID":23759}],"Thumbnail":null,"ID":154568},{"Name":"Quantum Mechanics","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Wave-Particle Duality","Duration":"7m 3s","ChapterTopicVideoID":20158,"CourseChapterTopicPlaylistID":154569,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20158.jpeg","UploadDate":"2019-07-10T23:26:55.9470000","DurationForVideoObject":"PT7M3S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.965","Text":"In the previous videos,"},{"Start":"00:01.965 ","End":"00:04.845","Text":"we talked about the Bohr model of the hydrogen atom."},{"Start":"00:04.845 ","End":"00:10.365","Text":"In this video we\u0027ll talk about the foundations of quantum theory as we know it nowadays."},{"Start":"00:10.365 ","End":"00:15.690","Text":"Let\u0027s begin by describing some of the successes and failures of the Bohr model."},{"Start":"00:15.690 ","End":"00:19.020","Text":"The Bohr model gives the correct energy levels and the emission"},{"Start":"00:19.020 ","End":"00:23.235","Text":"spectrum for hydrogen and hydrogen-like ions."},{"Start":"00:23.235 ","End":"00:26.718","Text":"Those are ions that have only one electron."},{"Start":"00:26.718 ","End":"00:30.320","Text":"Then we get En is equal to minus R_H,"},{"Start":"00:30.320 ","End":"00:32.795","Text":"which is the Rydberg constant, times Z^2,"},{"Start":"00:32.795 ","End":"00:36.715","Text":"where Z is the atomic number, divided by n^2."},{"Start":"00:36.715 ","End":"00:41.479","Text":"It gives the correct energy levels for hydrogen-like ions,"},{"Start":"00:41.479 ","End":"00:44.270","Text":"but not for other atoms."},{"Start":"00:44.270 ","End":"00:46.640","Text":"For other atoms it fails."},{"Start":"00:46.640 ","End":"00:50.150","Text":"In addition, there\u0027s no fundamental basis for"},{"Start":"00:50.150 ","End":"00:55.175","Text":"electrons moving in circular orbits or any well-defined orbit."},{"Start":"00:55.175 ","End":"00:56.900","Text":"In fact we\u0027ll see later on,"},{"Start":"00:56.900 ","End":"01:01.970","Text":"these electrons don\u0027t move in well-defined orbits at all."},{"Start":"01:01.970 ","End":"01:05.345","Text":"Now there are 2 main ideas that led to quantum mechanics."},{"Start":"01:05.345 ","End":"01:08.150","Text":"The first is wave-particle duality,"},{"Start":"01:08.150 ","End":"01:10.480","Text":"which we\u0027ll describe in this video,"},{"Start":"01:10.480 ","End":"01:15.380","Text":"and the second one is the Heisenberg uncertainty principle,"},{"Start":"01:15.380 ","End":"01:18.830","Text":"which we\u0027ll talk about in the next video."},{"Start":"01:18.830 ","End":"01:21.545","Text":"What\u0027s wave-particle duality?"},{"Start":"01:21.545 ","End":"01:23.990","Text":"This says that light can behave as"},{"Start":"01:23.990 ","End":"01:28.550","Text":"either a particle or as a wave depending on the experiment."},{"Start":"01:28.550 ","End":"01:31.925","Text":"For example, where light is dispersed by prism,"},{"Start":"01:31.925 ","End":"01:33.920","Text":"we saw that we got all different colors,"},{"Start":"01:33.920 ","End":"01:35.815","Text":"all the colors of the rainbow,"},{"Start":"01:35.815 ","End":"01:37.730","Text":"here it behaves like a wave."},{"Start":"01:37.730 ","End":"01:41.866","Text":"When light undergoes constructive or destructive interference,"},{"Start":"01:41.866 ","End":"01:43.775","Text":"it again behaves like a wave."},{"Start":"01:43.775 ","End":"01:52.980","Text":"Another case where it behaves like a wave is when is light approaching an aperture,"},{"Start":"01:52.980 ","End":"01:56.155","Text":"a little hole in a screen."},{"Start":"01:56.155 ","End":"02:03.145","Text":"Then as the light goes through the whole it spreads out in circular waves."},{"Start":"02:03.145 ","End":"02:06.920","Text":"This process is called diffraction."},{"Start":"02:09.540 ","End":"02:12.130","Text":"In all these cases,"},{"Start":"02:12.130 ","End":"02:13.915","Text":"light behaves like a wave."},{"Start":"02:13.915 ","End":"02:15.575","Text":"What about a particle?"},{"Start":"02:15.575 ","End":"02:20.350","Text":"We\u0027ve met several cases already where light is emitted by an atom."},{"Start":"02:20.350 ","End":"02:22.855","Text":"We saw that comes out like a photon."},{"Start":"02:22.855 ","End":"02:25.840","Text":"A whole bundle of energy comes out one time,"},{"Start":"02:25.840 ","End":"02:31.760","Text":"that\u0027s a photon with energy E=h Nu."},{"Start":"02:31.760 ","End":"02:35.530","Text":"We also saw that in the photoelectric effect,"},{"Start":"02:35.530 ","End":"02:46.385","Text":"light in photons hit a metal screen and then electrons are emitted."},{"Start":"02:46.385 ","End":"02:53.930","Text":"Each photon of the appropriate wavelength leads to the emission of an electron."},{"Start":"02:53.930 ","End":"02:59.780","Text":"What we see now is that light can behave either as a particle or a wave,"},{"Start":"02:59.780 ","End":"03:02.810","Text":"but it\u0027s more wide than that."},{"Start":"03:02.810 ","End":"03:08.565","Text":"We\u0027ll see in a minute that particles can also behave as waves."},{"Start":"03:08.565 ","End":"03:11.840","Text":"The person who discovered this was called De Broglie."},{"Start":"03:11.840 ","End":"03:20.635","Text":"He wrote a relation called De Broglie relation in 1924 and got the Nobel Prize for 1929."},{"Start":"03:20.635 ","End":"03:24.980","Text":"He was a prince, Louis de Broglie suggested that small particles,"},{"Start":"03:24.980 ","End":"03:28.685","Text":"such as electrons, have wave-like properties."},{"Start":"03:28.685 ","End":"03:30.920","Text":"Here\u0027s the De Broglie relation."},{"Start":"03:30.920 ","End":"03:35.675","Text":"The wavelength associated with a particle is equal to"},{"Start":"03:35.675 ","End":"03:41.840","Text":"the Planck\u0027s constant h divided by the mass of the particle times its velocity,"},{"Start":"03:41.840 ","End":"03:44.024","Text":"mv is called the momentum,"},{"Start":"03:44.024 ","End":"03:47.570","Text":"we write it as p. Lambda is equal to h"},{"Start":"03:47.570 ","End":"03:52.085","Text":"divided by p. We can see immediately from this relationship,"},{"Start":"03:52.085 ","End":"03:54.740","Text":"that if m is very large,"},{"Start":"03:54.740 ","End":"03:57.485","Text":"Lambda will be small."},{"Start":"03:57.485 ","End":"04:01.175","Text":"This is only important for very small particles."},{"Start":"04:01.175 ","End":"04:04.160","Text":"As soon as the particle is heavier with"},{"Start":"04:04.160 ","End":"04:08.480","Text":"such small Lambdas that it\u0027s impossible to see anything at all."},{"Start":"04:08.480 ","End":"04:10.205","Text":"Let\u0027s take an example."},{"Start":"04:10.205 ","End":"04:13.700","Text":"What is the wavelength associated with electrons that"},{"Start":"04:13.700 ","End":"04:18.440","Text":"travels the velocity 3 times 10^6 meters per second?"},{"Start":"04:18.440 ","End":"04:20.600","Text":"That\u0027s a very fast electron."},{"Start":"04:20.600 ","End":"04:24.570","Text":"That\u0027s a hundreds of the speed of light."},{"Start":"04:26.470 ","End":"04:29.570","Text":"C, the speed of light."},{"Start":"04:29.570 ","End":"04:35.540","Text":"The wavelength is equal to h divided by m times v. Planck\u0027s constant is"},{"Start":"04:35.540 ","End":"04:42.795","Text":"6.626 times 10^ minus 34 joules times second."},{"Start":"04:42.795 ","End":"04:50.025","Text":"Here I\u0027ve written the joule was kilogram times meter squared times second power minus 2."},{"Start":"04:50.025 ","End":"04:51.860","Text":"Now, this is divided by the mass,"},{"Start":"04:51.860 ","End":"04:54.635","Text":"and we also write the mass of the electron in kilograms,"},{"Start":"04:54.635 ","End":"05:00.505","Text":"9.1 or 9 times 10^minus31 kilograms."},{"Start":"05:00.505 ","End":"05:07.700","Text":"Then the velocity is 3.00 times 10^6 meters per second."},{"Start":"05:07.700 ","End":"05:09.925","Text":"Now we have to work this out,"},{"Start":"05:09.925 ","End":"05:13.315","Text":"kilogram cancels with kilogram."},{"Start":"05:13.315 ","End":"05:16.360","Text":"Seconds, the power of minus 2 times second,"},{"Start":"05:16.360 ","End":"05:18.270","Text":"is second power minus 1,"},{"Start":"05:18.270 ","End":"05:21.620","Text":"that cancels per second to borrow minus 1."},{"Start":"05:21.620 ","End":"05:25.910","Text":"In the denominator, we have meters squared divided by meters,"},{"Start":"05:25.910 ","End":"05:29.840","Text":"so we\u0027re left with meter in the numerator."},{"Start":"05:29.840 ","End":"05:32.000","Text":"When we work out the,"},{"Start":"05:32.000 ","End":"05:37.565","Text":"we get 0.242 times 10^minus 9 meters."},{"Start":"05:37.565 ","End":"05:43.400","Text":"That 0.242 nanometers."},{"Start":"05:43.400 ","End":"05:46.700","Text":"That\u0027s a very small wavelength."},{"Start":"05:46.700 ","End":"05:50.685","Text":"We can also write that as 242 picometers,"},{"Start":"05:50.685 ","End":"05:55.630","Text":"where picometer is 10^minus 12 meters."},{"Start":"05:55.630 ","End":"05:59.410","Text":"Here we have a very small wavelength."},{"Start":"05:59.410 ","End":"06:03.250","Text":"This is a very short wavelengths, so high-speed electrons,"},{"Start":"06:03.250 ","End":"06:06.130","Text":"electrons that are proceeding at"},{"Start":"06:06.130 ","End":"06:11.605","Text":"a very high speed can be used instead of light in microscopy,"},{"Start":"06:11.605 ","End":"06:14.275","Text":"we call this electron microscope."},{"Start":"06:14.275 ","End":"06:17.785","Text":"There are all sorts of electron microscopes nowadays."},{"Start":"06:17.785 ","End":"06:22.270","Text":"They give very precise pictures and just as X-rays,"},{"Start":"06:22.270 ","End":"06:24.475","Text":"which are electromagnetic radiation,"},{"Start":"06:24.475 ","End":"06:26.698","Text":"can use to determine the structure of crystals,"},{"Start":"06:26.698 ","End":"06:29.530","Text":"because they have very small wavelengths,"},{"Start":"06:29.530 ","End":"06:32.292","Text":"we call it X-ray diffraction,"},{"Start":"06:32.292 ","End":"06:36.145","Text":"so can electrons be used to study crystals,"},{"Start":"06:36.145 ","End":"06:38.335","Text":"we call electron diffraction."},{"Start":"06:38.335 ","End":"06:41.270","Text":"It was first demonstrated by Davisson and Germer."},{"Start":"06:41.270 ","End":"06:46.880","Text":"This convinced people that electrons behave like waves."},{"Start":"06:46.880 ","End":"06:56.760","Text":"In this video, we discussed wave particle duality for both light and particles."},{"Start":"06:56.760 ","End":"07:01.060","Text":"Very fundamental concept."}],"ID":20948},{"Watched":false,"Name":"Heisenberg Uncertainty Principle","Duration":"6m 54s","ChapterTopicVideoID":20159,"CourseChapterTopicPlaylistID":154569,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20159.jpeg","UploadDate":"2019-08-31T23:56:40.5370000","DurationForVideoObject":"PT6M54S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.515","Text":"In the previous video,"},{"Start":"00:01.515 ","End":"00:04.140","Text":"we talked about the wave particle duality."},{"Start":"00:04.140 ","End":"00:08.242","Text":"This video, we\u0027ll talk about the Heisenberg uncertainty principle,"},{"Start":"00:08.242 ","End":"00:11.670","Text":"another of the ideas that led to quantum mechanics."},{"Start":"00:11.670 ","End":"00:16.470","Text":"First, let\u0027s talk about the motion of an object according to classical mechanics."},{"Start":"00:16.470 ","End":"00:18.450","Text":"According to classical mechanics,"},{"Start":"00:18.450 ","End":"00:21.645","Text":"objects travel in a well-defined trajectory."},{"Start":"00:21.645 ","End":"00:26.220","Text":"At every moment we can calculate the position of the object and its momentum."},{"Start":"00:26.220 ","End":"00:33.090","Text":"Supposing we fire a missile we can use classical mechanics to calculate"},{"Start":"00:33.090 ","End":"00:40.405","Text":"its flight path and to know precisely when and where the missile will land."},{"Start":"00:40.405 ","End":"00:42.550","Text":"This is true for large objects,"},{"Start":"00:42.550 ","End":"00:46.370","Text":"but not for very small particles such as electrons."},{"Start":"00:46.370 ","End":"00:50.255","Text":"This is expressed in the Heisenberg uncertainty principle,"},{"Start":"00:50.255 ","End":"00:57.040","Text":"which was written by Heisenberg in 1927. What does it say?"},{"Start":"00:57.040 ","End":"01:05.100","Text":"It says that Delta x times Delta p is greater or equal to h,"},{"Start":"01:05.100 ","End":"01:08.095","Text":"that\u0027s Planck\u0027s constant divided by 4Pi."},{"Start":"01:08.095 ","End":"01:13.490","Text":"Now Delta x is the uncertainty in position of a particle, and Delta p,"},{"Start":"01:13.490 ","End":"01:18.325","Text":"which is equal to mass times the uncertainty in the velocity,"},{"Start":"01:18.325 ","End":"01:20.745","Text":"is the uncertainty in its momentum."},{"Start":"01:20.745 ","End":"01:26.350","Text":"This says that the uncertainty in position times the uncertainty in"},{"Start":"01:26.350 ","End":"01:31.885","Text":"momentum is greater or equal to h divided by 4Pi."},{"Start":"01:31.885 ","End":"01:33.430","Text":"What does this all mean?"},{"Start":"01:33.430 ","End":"01:37.420","Text":"It means that if Delta x is small,"},{"Start":"01:37.420 ","End":"01:40.090","Text":"Delta p will be large."},{"Start":"01:40.090 ","End":"01:41.680","Text":"In order to understand this,"},{"Start":"01:41.680 ","End":"01:43.735","Text":"it\u0027s best to take equality."},{"Start":"01:43.735 ","End":"01:46.164","Text":"Delta x is small."},{"Start":"01:46.164 ","End":"01:52.900","Text":"Delta p has to be large so that the multiplication of the 2 is equal to h over 4Pi."},{"Start":"01:52.900 ","End":"01:56.005","Text":"On the other hand, if Delta p is small,"},{"Start":"01:56.005 ","End":"01:58.305","Text":"Delta x must be large."},{"Start":"01:58.305 ","End":"02:02.885","Text":"What\u0027s for sure they both can\u0027t be small at the same time."},{"Start":"02:02.885 ","End":"02:08.585","Text":"That means that we cannot know the position and momentum of a particle simultaneously."},{"Start":"02:08.585 ","End":"02:11.255","Text":"Now, this has enormous repercussions."},{"Start":"02:11.255 ","End":"02:14.419","Text":"It means that there are no well-defined trajectories"},{"Start":"02:14.419 ","End":"02:17.540","Text":"of small particles such as electrons."},{"Start":"02:17.540 ","End":"02:23.245","Text":"We can\u0027t know that electron moves the circle, as Bohr suggested."},{"Start":"02:23.245 ","End":"02:26.780","Text":"Now h over 4Pi is are very small number."},{"Start":"02:26.780 ","End":"02:29.915","Text":"For large particles, it\u0027s almost 0."},{"Start":"02:29.915 ","End":"02:35.584","Text":"That means that the uncertainty principle doesn\u0027t apply to macroscopic objects."},{"Start":"02:35.584 ","End":"02:42.769","Text":"Delta x and Delta p can both be very small at the same time for macroscopic objects."},{"Start":"02:42.769 ","End":"02:44.975","Text":"Now how are we going to explain all this?"},{"Start":"02:44.975 ","End":"02:48.140","Text":"We can explain it in terms of wave packets."},{"Start":"02:48.140 ","End":"02:50.735","Text":"Remember that according to De Broglie,"},{"Start":"02:50.735 ","End":"02:53.600","Text":"particles have wave properties."},{"Start":"02:53.600 ","End":"02:58.860","Text":"Now, wave is not located at any particular point in space."},{"Start":"02:59.140 ","End":"03:01.670","Text":"Let\u0027s consider a wave,"},{"Start":"03:01.670 ","End":"03:04.505","Text":"and this time I\u0027ve chosen a cosine wave,"},{"Start":"03:04.505 ","End":"03:11.150","Text":"cosine kx, where k is 2Pi p/h."},{"Start":"03:11.150 ","End":"03:14.558","Text":"In other words, k is proportional to the moment."},{"Start":"03:14.558 ","End":"03:16.310","Text":"It\u0027s called the wave vector."},{"Start":"03:16.310 ","End":"03:19.135","Text":"We\u0027ll see the moment why it\u0027s called the wave vector."},{"Start":"03:19.135 ","End":"03:26.095","Text":"K is 2Pi over h times p. We could write that as p divided by h-bar."},{"Start":"03:26.095 ","End":"03:32.150","Text":"H-bar is very useful and it\u0027s equal to h divided by 2Pi."},{"Start":"03:32.150 ","End":"03:36.670","Text":"We can write the k is equal to p divided by h-bar."},{"Start":"03:36.670 ","End":"03:38.890","Text":"If we go back to this,"},{"Start":"03:38.890 ","End":"03:41.740","Text":"we\u0027re writing it 2Pi p/h."},{"Start":"03:41.740 ","End":"03:44.290","Text":"We can write 2Pi over h,"},{"Start":"03:44.290 ","End":"03:47.350","Text":"and then we can write p according to De Broglie."},{"Start":"03:47.350 ","End":"03:51.025","Text":"According to De Broglie, p is equal to h over Lambda."},{"Start":"03:51.025 ","End":"03:57.175","Text":"The numerator and denominator cancel and we\u0027re left with 2Pi over Lambda."},{"Start":"03:57.175 ","End":"04:01.525","Text":"K is inversely proportional to the wavelength,"},{"Start":"04:01.525 ","End":"04:03.889","Text":"and it\u0027s called the wave vector,"},{"Start":"04:03.889 ","End":"04:07.289","Text":"and as a wavelength has units of meters,"},{"Start":"04:07.289 ","End":"04:11.240","Text":"then k has units of meters to the power minus 1."},{"Start":"04:11.240 ","End":"04:13.535","Text":"We\u0027re going to consider 2 cases."},{"Start":"04:13.535 ","End":"04:14.990","Text":"These are wave packets."},{"Start":"04:14.990 ","End":"04:22.070","Text":"Wave packets are the sums of separate waves."},{"Start":"04:22.070 ","End":"04:24.080","Text":"Here we have 2 wave packets."},{"Start":"04:24.080 ","End":"04:25.595","Text":"In the first one,"},{"Start":"04:25.595 ","End":"04:28.430","Text":"we have cosine 1.8x."},{"Start":"04:28.430 ","End":"04:33.855","Text":"That means k is=1.8 plus cosine of 1.9x,"},{"Start":"04:33.855 ","End":"04:39.540","Text":"that\u0027s k=1.9 plus the cosine of 2x, that\u0027s k=2."},{"Start":"04:39.540 ","End":"04:44.400","Text":"Then plus cosine of 2.1x plus cosine of 2.2x."},{"Start":"04:44.400 ","End":"04:48.695","Text":"The average value of k is 2."},{"Start":"04:48.695 ","End":"04:53.560","Text":"We have a whole range of ks from 1.8-2.2."},{"Start":"04:53.560 ","End":"05:02.625","Text":"We can say that Delta k is equal to 2.2 minus 1.8 equal to 0.4."},{"Start":"05:02.625 ","End":"05:06.490","Text":"The second case we\u0027re going to consider is the same thing."},{"Start":"05:06.490 ","End":"05:09.130","Text":"The average will be k=2."},{"Start":"05:09.130 ","End":"05:11.005","Text":"But we have a different distribution."},{"Start":"05:11.005 ","End":"05:17.375","Text":"We go from 1.6k=1.6 to k equals 2.4."},{"Start":"05:17.375 ","End":"05:20.700","Text":"Delta k is larger in this case."},{"Start":"05:20.700 ","End":"05:25.515","Text":"It\u0027s 2.4 minus 1.6 that\u0027s 0.8."},{"Start":"05:25.515 ","End":"05:30.940","Text":"Here are 2 wave packets, this is x."},{"Start":"05:32.600 ","End":"05:38.965","Text":"Up here is the amplitude of the waves."},{"Start":"05:38.965 ","End":"05:40.930","Text":"Here we\u0027ve drawn the colors,"},{"Start":"05:40.930 ","End":"05:42.400","Text":"all the different waves,"},{"Start":"05:42.400 ","End":"05:44.800","Text":"the 5 waves that we\u0027re adding together."},{"Start":"05:44.800 ","End":"05:47.335","Text":"In orange is the addition of the waves."},{"Start":"05:47.335 ","End":"05:49.370","Text":"That\u0027s the wave packet,"},{"Start":"05:49.370 ","End":"05:50.860","Text":"and the right-hand side,"},{"Start":"05:50.860 ","End":"05:53.890","Text":"is a second wave packet, the left-hand side,"},{"Start":"05:53.890 ","End":"05:58.050","Text":"Delta k is 0.4."},{"Start":"05:58.050 ","End":"06:02.925","Text":"The right-hand side, Delta k is 0.8."},{"Start":"06:02.925 ","End":"06:05.320","Text":"Now let\u0027s look at Delta x."},{"Start":"06:05.320 ","End":"06:10.130","Text":"We see here a much wider distribution of Delta x,"},{"Start":"06:10.130 ","End":"06:14.270","Text":"Delta x is much greater than the right-hand side,"},{"Start":"06:14.270 ","End":"06:17.330","Text":"where the particle is much more localized."},{"Start":"06:17.330 ","End":"06:23.015","Text":"Here, Delta x is greater than on the right-hand side,"},{"Start":"06:23.015 ","End":"06:27.410","Text":"and Delta k is greater on the right-hand side."},{"Start":"06:27.410 ","End":"06:32.720","Text":"What we have, we can see that where Delta k is greater,"},{"Start":"06:32.720 ","End":"06:35.209","Text":"Delta x is smaller."},{"Start":"06:35.209 ","End":"06:38.585","Text":"That\u0027s exactly what Heisenberg told us."},{"Start":"06:38.585 ","End":"06:40.310","Text":"To summarize, Delta k,"},{"Start":"06:40.310 ","End":"06:42.365","Text":"which is Delta p,"},{"Start":"06:42.365 ","End":"06:48.019","Text":"is larger, and Delta h is smaller than the right-hand side graph."},{"Start":"06:48.019 ","End":"06:54.750","Text":"In this video, we\u0027ve talked above the Heisenberg uncertainty principle."}],"ID":20949},{"Watched":false,"Name":"Schrodinger Equation","Duration":"5m ","ChapterTopicVideoID":20160,"CourseChapterTopicPlaylistID":154569,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20160.jpeg","UploadDate":"2019-07-10T23:29:58.3700000","DurationForVideoObject":"PT5M","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.405","Text":"In this video, we\u0027ll talk about the Schrodinger equation."},{"Start":"00:03.405 ","End":"00:07.260","Text":"The Schrodinger equation was first formulated in 1927"},{"Start":"00:07.260 ","End":"00:12.330","Text":"by Erwin Schrodinger and he got Nobel Prize for it in 1933."},{"Start":"00:12.330 ","End":"00:16.830","Text":"Schrodinger equation is the main equation of modern quantum chemistry."},{"Start":"00:16.830 ","End":"00:20.189","Text":"It can only be solved exactly for a few problems,"},{"Start":"00:20.189 ","End":"00:25.870","Text":"but it can be solved using approximations for a vast number of problems."},{"Start":"00:26.480 ","End":"00:32.240","Text":"The simplest way to write it is HPsi=EPsi."},{"Start":"00:32.240 ","End":"00:34.145","Text":"Will see this looks very simple,"},{"Start":"00:34.145 ","End":"00:37.120","Text":"but in fact it\u0027s rather complicated equation."},{"Start":"00:37.120 ","End":"00:41.360","Text":"H is called the Hamiltonian and it\u0027s a mathematical operator."},{"Start":"00:41.360 ","End":"00:45.440","Text":"We offer right with a hat to indicate that it\u0027s an operator."},{"Start":"00:45.440 ","End":"00:49.745","Text":"E is the eigenvalue that gives us the energy levels,"},{"Start":"00:49.745 ","End":"00:58.335","Text":"and Greek letter Psi is the wavefunction or eigenfunction."},{"Start":"00:58.335 ","End":"01:03.050","Text":"It\u0027s called the wavefunction to remind us of the wave particle duality."},{"Start":"01:03.050 ","End":"01:07.010","Text":"There\u0027s a particle can be also act like a wave."},{"Start":"01:07.010 ","End":"01:10.190","Text":"Often there are several solutions to this equation,"},{"Start":"01:10.190 ","End":"01:16.050","Text":"and then we write it HPsi_n=E_nPsi_ n."},{"Start":"01:16.050 ","End":"01:23.105","Text":"Psi_1 would be the wave function and E_1 would be its energy,"},{"Start":"01:23.105 ","End":"01:25.205","Text":"and so on, so forth."},{"Start":"01:25.205 ","End":"01:27.890","Text":"Now, let\u0027s discuss the Hamiltonian."},{"Start":"01:27.890 ","End":"01:35.735","Text":"The Hamiltonian is mathematical operator related to the energy."},{"Start":"01:35.735 ","End":"01:40.745","Text":"It can be written as an operator for the kinetic energy,"},{"Start":"01:40.745 ","End":"01:43.865","Text":"plus an operator for the potential energy."},{"Start":"01:43.865 ","End":"01:46.430","Text":"Let\u0027s look at the kinetic energy first."},{"Start":"01:46.430 ","End":"01:49.895","Text":"For a 1 dimensional time-independent problem."},{"Start":"01:49.895 ","End":"01:55.180","Text":"The operator of the kinetic energy can be written as minus h-bar^2"},{"Start":"01:55.180 ","End":"02:02.230","Text":"over 2m times d^2 dx^2 in other words,"},{"Start":"02:02.230 ","End":"02:05.590","Text":"minus h-bar^2 over 2m,"},{"Start":"02:05.590 ","End":"02:12.455","Text":"where m is the mass of the particle times the second derivative with respect to x."},{"Start":"02:12.455 ","End":"02:18.590","Text":"If we write out h-bar as h over 2Pi,"},{"Start":"02:18.590 ","End":"02:23.050","Text":"we can rewrite that as minus h^2 over"},{"Start":"02:23.050 ","End":"02:29.485","Text":"8Pi^2m times the second derivative with respect to x."},{"Start":"02:29.485 ","End":"02:32.410","Text":"Now second derivative with respect to x,"},{"Start":"02:32.410 ","End":"02:35.120","Text":"has to act on something."},{"Start":"02:35.120 ","End":"02:40.870","Text":"We see in the equation that it act on Psi the wavefunction."},{"Start":"02:40.870 ","End":"02:47.120","Text":"Expression for the potential energy depends on which problem we want to solve."},{"Start":"02:47.120 ","End":"02:49.790","Text":"In summary, the Schrodinger equation is"},{"Start":"02:49.790 ","End":"02:55.025","Text":"a differential equation that can all be solved exactly for a few problems."},{"Start":"02:55.025 ","End":"02:56.480","Text":"Now in the following videos,"},{"Start":"02:56.480 ","End":"02:59.810","Text":"we\u0027re going to discuss 2 problems where it can be sold."},{"Start":"02:59.810 ","End":"03:02.330","Text":"The first one is the particle in a box."},{"Start":"03:02.330 ","End":"03:06.125","Text":"This is a simplest possible 1 dimensional problem."},{"Start":"03:06.125 ","End":"03:08.300","Text":"We\u0027ll talk about that in the next video."},{"Start":"03:08.300 ","End":"03:10.910","Text":"We won\u0027t actually solve the Schrodinger equation,"},{"Start":"03:10.910 ","End":"03:13.330","Text":"we\u0027ll just discuss the solutions."},{"Start":"03:13.330 ","End":"03:16.715","Text":"After that, we\u0027ll discuss the hydrogen atom,"},{"Start":"03:16.715 ","End":"03:19.630","Text":"which is a 3 dimensional problem."},{"Start":"03:19.630 ","End":"03:23.560","Text":"The electron can move in 3 dimensions,"},{"Start":"03:23.560 ","End":"03:26.525","Text":"and that will be after the particle in a box."},{"Start":"03:26.525 ","End":"03:30.890","Text":"Now it\u0027s a very important problem to interpret Psi."},{"Start":"03:30.890 ","End":"03:33.440","Text":"What is interpretation of Psi?"},{"Start":"03:33.440 ","End":"03:38.914","Text":"Usually, we talked about Psi^2 the interpretation of Psi^2,"},{"Start":"03:38.914 ","End":"03:42.805","Text":"which is more obvious than that of Psi."},{"Start":"03:42.805 ","End":"03:45.840","Text":"The probability to find the particle,"},{"Start":"03:45.840 ","End":"03:51.890","Text":"in the little area between x and x plus dx is little range."},{"Start":"03:51.890 ","End":"03:59.840","Text":"Dx is given by the absolute value squared of Psi times dx."},{"Start":"03:59.840 ","End":"04:05.670","Text":"Psi absolute value squared of Psi will always be positive."},{"Start":"04:07.000 ","End":"04:10.010","Text":"Probability must be positive."},{"Start":"04:10.010 ","End":"04:17.720","Text":"The probability is absolute volume of Psi squared of that times dx."},{"Start":"04:17.720 ","End":"04:23.705","Text":"The absolute value squared of Psi itself is called the probability density."},{"Start":"04:23.705 ","End":"04:25.760","Text":"When it\u0027s multiplied by dx,"},{"Start":"04:25.760 ","End":"04:27.500","Text":"we get the probability."},{"Start":"04:27.500 ","End":"04:29.720","Text":"In quantum mechanics, we only know"},{"Start":"04:29.720 ","End":"04:32.840","Text":"the probability to find the particle in a particular position."},{"Start":"04:32.840 ","End":"04:35.585","Text":"That\u0027s the Heisenberg uncertainty principle."},{"Start":"04:35.585 ","End":"04:41.330","Text":"We\u0027ll see that we\u0027ll only know approximately where the particle is,"},{"Start":"04:41.330 ","End":"04:44.620","Text":"where the electron is and the hydrogen atom, for example."},{"Start":"04:44.620 ","End":"04:52.205","Text":"We cannot know its exact orbit like we knew according to classical theory."},{"Start":"04:52.205 ","End":"04:58.235","Text":"In this video, we talked about the Schrodinger equation and the following videos,"},{"Start":"04:58.235 ","End":"05:00.959","Text":"we\u0027ll talk about their solution."}],"ID":20950},{"Watched":false,"Name":"Particle in a Box","Duration":"8m 5s","ChapterTopicVideoID":20161,"CourseChapterTopicPlaylistID":154569,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20161.jpeg","UploadDate":"2019-07-10T23:32:25.0000000","DurationForVideoObject":"PT8M5S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.785","Text":"In the previous video,"},{"Start":"00:01.785 ","End":"00:04.065","Text":"we talked about the Schrodinger equation."},{"Start":"00:04.065 ","End":"00:08.730","Text":"In this video, we\u0027ll discuss its solution for the particle in a box."},{"Start":"00:08.730 ","End":"00:10.965","Text":"What\u0027s a particle in a box?"},{"Start":"00:10.965 ","End":"00:18.420","Text":"This is a particle of mass m that\u0027s free to move between x=0 and x=L,"},{"Start":"00:18.420 ","End":"00:24.345","Text":"but not beyond 0 or beyond L. It\u0027s a 1 dimensional problem."},{"Start":"00:24.345 ","End":"00:31.169","Text":"Here\u0027s a picture. The potential energy is between 0 and L. It\u0027s is 0."},{"Start":"00:31.169 ","End":"00:34.570","Text":"We\u0027ve written that here, V equals 0."},{"Start":"00:35.060 ","End":"00:40.310","Text":"When x is smaller than 0 or x is greater than L,"},{"Start":"00:40.310 ","End":"00:43.760","Text":"the potential energy is infinity."},{"Start":"00:43.760 ","End":"00:45.710","Text":"Why is it called a particle in a box?"},{"Start":"00:45.710 ","End":"00:52.920","Text":"It\u0027s called a particle box because this shape is reminiscent of a box."},{"Start":"00:52.920 ","End":"00:55.410","Text":"It\u0027s really a 1 dimensional problem."},{"Start":"00:55.410 ","End":"01:00.635","Text":"Now we can solve Schrodinger equation quite easily for this particular problem,"},{"Start":"01:00.635 ","End":"01:03.965","Text":"because the potential energy is 0 within the box."},{"Start":"01:03.965 ","End":"01:08.810","Text":"But here we\u0027re going to just give the wavefunctions and energy levels."},{"Start":"01:08.810 ","End":"01:14.435","Text":"Psi n is equal to the square root of 2 over L,"},{"Start":"01:14.435 ","End":"01:16.175","Text":"where L is length of the box,"},{"Start":"01:16.175 ","End":"01:19.730","Text":"sine nPix over L,"},{"Start":"01:19.730 ","End":"01:22.160","Text":"where n is the quantum number"},{"Start":"01:22.160 ","End":"01:29.120","Text":"and E_n is equal"},{"Start":"01:29.120 ","End":"01:34.960","Text":"to n^2 h^2 over 8mL^2."},{"Start":"01:34.960 ","End":"01:37.545","Text":"If Psi 1 has energy E_1,"},{"Start":"01:37.545 ","End":"01:41.205","Text":"psi 2 has the energy E_2, and so on."},{"Start":"01:41.205 ","End":"01:47.010","Text":"E_1 is equal to h^2 over 8mL^2 and"},{"Start":"01:47.010 ","End":"01:52.830","Text":"E_2 is equal to 4h^2 over 8mL^2 and so on."},{"Start":"01:52.830 ","End":"01:57.015","Text":"E_3 is equal to 9h^2 over 8mL^2."},{"Start":"01:57.015 ","End":"02:00.680","Text":"Now, if we look at the difference between E_2 and E_1,"},{"Start":"02:00.680 ","End":"02:07.105","Text":"we see it\u0027s 3 times h^2 over 8mL^2."},{"Start":"02:07.105 ","End":"02:15.485","Text":"Whereas the difference between E_3 and E_2 is 5h^2 over 8mL^2."},{"Start":"02:15.485 ","End":"02:23.060","Text":"The difference is, the gaps between the levels grow as n gets higher."},{"Start":"02:23.060 ","End":"02:26.165","Text":"Now here I\u0027ve drawn the wave functions."},{"Start":"02:26.165 ","End":"02:31.370","Text":"This is a drawings of Psi between 0 and L. I\u0027ve"},{"Start":"02:31.370 ","End":"02:37.130","Text":"moved the wave functions up so that you can see them each clearly."},{"Start":"02:37.130 ","End":"02:42.747","Text":"The first one is n equal to 1, that\u0027s Psi 1."},{"Start":"02:42.747 ","End":"02:46.365","Text":"Then, here\u0027s Psi 2,"},{"Start":"02:46.365 ","End":"02:49.875","Text":"Psi 3, and Psi 4."},{"Start":"02:49.875 ","End":"02:53.370","Text":"The energies, of course are E_1,"},{"Start":"02:53.370 ","End":"02:57.825","Text":"E_2, E_3, and E_4."},{"Start":"02:57.825 ","End":"03:01.665","Text":"Each 1 is 0 at 0,"},{"Start":"03:01.665 ","End":"03:03.930","Text":"x equal to 0,"},{"Start":"03:03.930 ","End":"03:12.065","Text":"and 0 at x equal to L. What can we see in this diagram?"},{"Start":"03:12.065 ","End":"03:16.760","Text":"First thing to note is a 1 dimensional problem so it has only 1 quantum number,"},{"Start":"03:16.760 ","End":"03:19.590","Text":"n. If it were 3 dimensional problem,"},{"Start":"03:19.590 ","End":"03:22.110","Text":"it would have 3 quantum numbers."},{"Start":"03:22.110 ","End":"03:24.290","Text":"Now the energy is quantized."},{"Start":"03:24.290 ","End":"03:26.930","Text":"We see only certain energies are allowed,"},{"Start":"03:26.930 ","End":"03:28.880","Text":"not all energies, just E_1,"},{"Start":"03:28.880 ","End":"03:31.210","Text":"E_2, E_3, E_4 and so on."},{"Start":"03:31.210 ","End":"03:33.860","Text":"The energy is quantized."},{"Start":"03:33.860 ","End":"03:42.575","Text":"We saw that the wave function Psi is 0 at x=0 and at x=L."},{"Start":"03:42.575 ","End":"03:44.960","Text":"For example here is 0,"},{"Start":"03:44.960 ","End":"03:47.315","Text":"0 and 0,"},{"Start":"03:47.315 ","End":"03:50.195","Text":"but it\u0027s 0 in other places as well."},{"Start":"03:50.195 ","End":"03:52.490","Text":"If we look at Psi 1,"},{"Start":"03:52.490 ","End":"03:56.825","Text":"we see that it\u0027s only 0 at 0 and L,"},{"Start":"03:56.825 ","End":"03:58.115","Text":"nothing in the middle."},{"Start":"03:58.115 ","End":"04:00.005","Text":"But if we look up Psi 2,"},{"Start":"04:00.005 ","End":"04:03.270","Text":"we see it\u0027s also 0 in the middle."},{"Start":"04:03.270 ","End":"04:05.490","Text":"If we look at Psi 3,"},{"Start":"04:05.490 ","End":"04:08.980","Text":"we see it\u0027s 0 at 2 places."},{"Start":"04:10.370 ","End":"04:14.385","Text":"Psi 4 is 0 at 3 places,"},{"Start":"04:14.385 ","End":"04:18.205","Text":"1, 2, 3."},{"Start":"04:18.205 ","End":"04:21.140","Text":"These places are called nodes."},{"Start":"04:21.140 ","End":"04:25.370","Text":"Places where the wave function is equal to 0 is called a node."},{"Start":"04:25.370 ","End":"04:29.780","Text":"The number of nodes as we can see is 0,"},{"Start":"04:29.780 ","End":"04:32.315","Text":"1, 2 and 3."},{"Start":"04:32.315 ","End":"04:35.345","Text":"That\u0027s equivalent to n minus 1,"},{"Start":"04:35.345 ","End":"04:37.360","Text":"so n is 4,"},{"Start":"04:37.360 ","End":"04:41.650","Text":"number of nodes is 3."},{"Start":"04:41.660 ","End":"04:45.180","Text":"That\u0027s what we see here, 1, 2, 3."},{"Start":"04:45.180 ","End":"04:47.150","Text":"Now, nodes are very important."},{"Start":"04:47.150 ","End":"04:51.785","Text":"We\u0027ll see where we draw the probability when we draw the square root of Psi,"},{"Start":"04:51.785 ","End":"04:55.550","Text":"that these are places where the probability is 0."},{"Start":"04:55.550 ","End":"04:58.490","Text":"We cannot find the particle at these points."},{"Start":"04:58.490 ","End":"05:03.575","Text":"Another point to note is that the energy levels are even or odd, even."},{"Start":"05:03.575 ","End":"05:06.139","Text":"Psi 1 is symmetric,"},{"Start":"05:06.139 ","End":"05:08.710","Text":"Psi 2 is anti-symmetric,"},{"Start":"05:08.710 ","End":"05:13.730","Text":"Psi 3 is symmetric and Psi 4 is anti-symmetric."},{"Start":"05:13.730 ","End":"05:15.230","Text":"What do we mean by symmetric?"},{"Start":"05:15.230 ","End":"05:18.710","Text":"We mean, say, here it\u0027s the same values here."},{"Start":"05:18.710 ","End":"05:21.170","Text":"Whereas for Psi 2,"},{"Start":"05:21.170 ","End":"05:23.510","Text":"here it\u0027s negative and here it\u0027s positive,"},{"Start":"05:23.510 ","End":"05:24.710","Text":"the same value,"},{"Start":"05:24.710 ","End":"05:26.980","Text":"negative and positive, and so on."},{"Start":"05:26.980 ","End":"05:30.185","Text":"Now let us look at the probability density."},{"Start":"05:30.185 ","End":"05:31.940","Text":"Here we see, of course,"},{"Start":"05:31.940 ","End":"05:34.775","Text":"that they\u0027re all symmetric because we\u0027ve taken the square."},{"Start":"05:34.775 ","End":"05:37.145","Text":"Where Psi was negative, it\u0027s now positive."},{"Start":"05:37.145 ","End":"05:39.350","Text":"Psi squared is positive."},{"Start":"05:39.350 ","End":"05:42.740","Text":"We can see also the nodes very clearly."},{"Start":"05:42.740 ","End":"05:46.580","Text":"You see here that in the center is 0,"},{"Start":"05:46.580 ","End":"05:50.765","Text":"there is 0 probability to find the particle there."},{"Start":"05:50.765 ","End":"05:53.015","Text":"Here is 0 and 0,"},{"Start":"05:53.015 ","End":"05:55.835","Text":"2 places where it\u0027s 0 probability,"},{"Start":"05:55.835 ","End":"05:58.180","Text":"and then 3 places."},{"Start":"05:58.180 ","End":"06:00.840","Text":"Here, of course, n is equal to 1,"},{"Start":"06:00.840 ","End":"06:03.730","Text":"2, 3 and 4."},{"Start":"06:03.730 ","End":"06:07.630","Text":"Another thing we can notice from here,"},{"Start":"06:07.630 ","End":"06:10.165","Text":"or perhaps more importantly,"},{"Start":"06:10.165 ","End":"06:12.155","Text":"from the previous diagram,"},{"Start":"06:12.155 ","End":"06:16.580","Text":"is that the waves look like standing waves in the string."},{"Start":"06:16.580 ","End":"06:18.755","Text":"As if we\u0027re holding a string."},{"Start":"06:18.755 ","End":"06:21.670","Text":"These are the possible standing waves."},{"Start":"06:21.670 ","End":"06:29.810","Text":"Then we can relate the wavelength of each wave to the length of the box."},{"Start":"06:29.810 ","End":"06:32.970","Text":"For example, the ground 1 Lambda,"},{"Start":"06:32.970 ","End":"06:34.635","Text":"we only get half of Lambda."},{"Start":"06:34.635 ","End":"06:37.840","Text":"Lambda is equal to 2L."},{"Start":"06:38.330 ","End":"06:40.395","Text":"The second one,"},{"Start":"06:40.395 ","End":"06:46.485","Text":"we have exactly Lambda equal to L. The third one,"},{"Start":"06:46.485 ","End":"06:51.540","Text":"we see 1.5 wavelengths."},{"Start":"06:51.540 ","End":"06:56.235","Text":"Lambda is equal to 2L over 3."},{"Start":"06:56.235 ","End":"07:02.830","Text":"The final one, Lambda is equal to L over 2."},{"Start":"07:02.830 ","End":"07:07.490","Text":"If we want a formula that includes all these possibilities and"},{"Start":"07:07.490 ","End":"07:11.765","Text":"we have Lambda is equal to 2L over n,"},{"Start":"07:11.765 ","End":"07:13.295","Text":"you\u0027ll see that works."},{"Start":"07:13.295 ","End":"07:14.810","Text":"Here n is 1,"},{"Start":"07:14.810 ","End":"07:17.860","Text":"n is 2, 3 and 4."},{"Start":"07:17.860 ","End":"07:22.925","Text":"Now, the maximum probability for n=1 is in the middle."},{"Start":"07:22.925 ","End":"07:25.400","Text":"This is a very much a quantum effect."},{"Start":"07:25.400 ","End":"07:28.100","Text":"You don\u0027t find this in classical mechanics at all."},{"Start":"07:28.100 ","End":"07:33.355","Text":"As n increases, the average probability becomes more uniform within the box."},{"Start":"07:33.355 ","End":"07:37.730","Text":"Now, here, you see it\u0027s a lot of ripples and the average is something like a half."},{"Start":"07:37.730 ","End":"07:39.485","Text":"If you go higher and higher,"},{"Start":"07:39.485 ","End":"07:42.670","Text":"it will be more like a half."},{"Start":"07:42.670 ","End":"07:45.110","Text":"That\u0027s a true in classical physics."},{"Start":"07:45.110 ","End":"07:47.810","Text":"In classical physics, the particle has"},{"Start":"07:47.810 ","End":"07:53.750","Text":"the same probability to be anywhere in the box because it\u0027s a free particle."},{"Start":"07:53.750 ","End":"07:57.844","Text":"Within the box, this particle is free."},{"Start":"07:57.844 ","End":"08:01.580","Text":"In this video, we discussed the particle in the box which"},{"Start":"08:01.580 ","End":"08:06.210","Text":"shows many features unique to quantum mechanics."}],"ID":20951}],"Thumbnail":null,"ID":154569},{"Name":"Electron Orbitals","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Wavefunction of H Atom 1","Duration":"5m 14s","ChapterTopicVideoID":20162,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20162.jpeg","UploadDate":"2019-08-26T09:37:06.8470000","DurationForVideoObject":"PT5M14S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.020 ","End":"00:02.100","Text":"In the previous video,"},{"Start":"00:02.100 ","End":"00:05.865","Text":"we discussed the Schrodinger equation for a particle in a box."},{"Start":"00:05.865 ","End":"00:11.235","Text":"In this video, we\u0027ll talk about the Schrodinger equation for the hydrogen atom."},{"Start":"00:11.235 ","End":"00:15.780","Text":"Going to talk about the Schrodinger equation for hydrogen-like species."},{"Start":"00:15.780 ","End":"00:20.712","Text":"That\u0027s any atom or ion that has only 1 electron."},{"Start":"00:20.712 ","End":"00:27.030","Text":"That\u0027s hydrogen, helium plus,"},{"Start":"00:27.030 ","End":"00:29.390","Text":"lithium 2 plus, and so on."},{"Start":"00:29.390 ","End":"00:31.700","Text":"As we\u0027ve said in a previous video,"},{"Start":"00:31.700 ","End":"00:35.630","Text":"what distinguishes the Schrodinger equation for 1 problem from"},{"Start":"00:35.630 ","End":"00:39.635","Text":"another problem is the expression for the potential energy."},{"Start":"00:39.635 ","End":"00:43.025","Text":"The expression for the kinetic energy is always the same."},{"Start":"00:43.025 ","End":"00:44.900","Text":"Now in this particular case,"},{"Start":"00:44.900 ","End":"00:50.970","Text":"the potential energy is that of an electron attracted to a nucleus with atomic number Z,"},{"Start":"00:50.970 ","End":"00:54.185","Text":"and we call this the Coulomb potential."},{"Start":"00:54.185 ","End":"01:04.195","Text":"Here\u0027s our electron with charge e and r nucleus with charge Ze times e plus."},{"Start":"01:04.195 ","End":"01:09.235","Text":"Just different sign, the opposite sign from the electronic charge,"},{"Start":"01:09.235 ","End":"01:15.370","Text":"and the distance between them is given by r. Now,"},{"Start":"01:15.370 ","End":"01:17.320","Text":"we can write this potential in this way."},{"Start":"01:17.320 ","End":"01:23.350","Text":"V the potential energy is a function of r is proportional to minus Z."},{"Start":"01:23.350 ","End":"01:27.820","Text":"Z is the atomic number times e squared,"},{"Start":"01:27.820 ","End":"01:31.075","Text":"where e is the electronic charge divided by"},{"Start":"01:31.075 ","End":"01:35.695","Text":"r. r is the distance of the electron from the nucleus,"},{"Start":"01:35.695 ","End":"01:37.555","Text":"as we pointed out already."},{"Start":"01:37.555 ","End":"01:41.150","Text":"Now, we can also draw this potential."},{"Start":"01:44.760 ","End":"01:50.110","Text":"This is r, and this is V(r),"},{"Start":"01:50.110 ","End":"01:53.030","Text":"we can draw it like this."},{"Start":"01:53.790 ","End":"01:56.287","Text":"It\u0027s always negative,"},{"Start":"01:56.287 ","End":"02:00.850","Text":"and when r is very large it gets to 0,"},{"Start":"02:00.850 ","End":"02:04.825","Text":"and when r is very small,"},{"Start":"02:04.825 ","End":"02:06.394","Text":"it goes to minus infinity."},{"Start":"02:06.394 ","End":"02:08.787","Text":"It goes down there to minus infinity,"},{"Start":"02:08.787 ","End":"02:12.438","Text":"and here it goes to 0."},{"Start":"02:12.438 ","End":"02:16.245","Text":"The electron is bound in this potential."},{"Start":"02:16.245 ","End":"02:20.920","Text":"Now we\u0027re going to talk about the coordinates that are suitable for this problem,"},{"Start":"02:20.920 ","End":"02:24.130","Text":"and they\u0027re called spherical polar coordinates."},{"Start":"02:24.130 ","End":"02:26.500","Text":"As the potential is spherical,"},{"Start":"02:26.500 ","End":"02:27.910","Text":"what does that mean?"},{"Start":"02:27.910 ","End":"02:30.460","Text":"It means that it only depends on r,"},{"Start":"02:30.460 ","End":"02:31.645","Text":"not on the angles,"},{"Start":"02:31.645 ","End":"02:33.520","Text":"is the same in any direction."},{"Start":"02:33.520 ","End":"02:37.060","Text":"Instead of using Cartesian coordinates as x, y, z,"},{"Start":"02:37.060 ","End":"02:41.695","Text":"we use the spherical polar coordinates r, Theta,"},{"Start":"02:41.695 ","End":"02:45.400","Text":"and Phi; where r is the distance,"},{"Start":"02:45.400 ","End":"02:47.283","Text":"this is the electron from the nucleus,"},{"Start":"02:47.283 ","End":"02:51.640","Text":"and Theta and Phi are angular coordinates."},{"Start":"02:51.640 ","End":"02:53.380","Text":"Let\u0027s see how they look."},{"Start":"02:53.380 ","End":"02:56.425","Text":"Here\u0027s the picture of the coordinates,"},{"Start":"02:56.425 ","End":"03:01.330","Text":"so r is the distance from the nucleus to the electron,"},{"Start":"03:01.330 ","End":"03:09.880","Text":"and the angle between r and the z-axis is called Theta."},{"Start":"03:09.880 ","End":"03:17.975","Text":"Now if we draw the projection of r onto the x-y plane that\u0027s here,"},{"Start":"03:17.975 ","End":"03:19.240","Text":"that\u0027s the projection,"},{"Start":"03:19.240 ","End":"03:25.960","Text":"then the angle between x and the projection is called Phi."},{"Start":"03:25.960 ","End":"03:29.240","Text":"These are 2 angular coordinates,"},{"Start":"03:29.240 ","End":"03:30.656","Text":"Theta and Phi,"},{"Start":"03:30.656 ","End":"03:35.000","Text":"and 1 distance r. Now just for the record,"},{"Start":"03:35.000 ","End":"03:39.083","Text":"r squared is equal to x squared plus y squared plus x squared,"},{"Start":"03:39.083 ","End":"03:42.560","Text":"and we can relate the Cartesian coordinates"},{"Start":"03:42.560 ","End":"03:46.515","Text":"with these spherical polar coordinates the following way."},{"Start":"03:46.515 ","End":"03:51.495","Text":"z is equal to r cosine Theta,"},{"Start":"03:51.495 ","End":"03:55.550","Text":"x is equal to r sin Theta cosine Phi,"},{"Start":"03:55.550 ","End":"03:59.615","Text":"and y is equal to r sin Theta sine Phi."},{"Start":"03:59.615 ","End":"04:01.715","Text":"We won\u0027t actually have to use this,"},{"Start":"04:01.715 ","End":"04:03.725","Text":"but it\u0027s a useful thing to know."},{"Start":"04:03.725 ","End":"04:06.484","Text":"Now, how do we write the wavefunctions?"},{"Start":"04:06.484 ","End":"04:09.140","Text":"Now in the case of hydrogen atom,"},{"Start":"04:09.140 ","End":"04:13.115","Text":"wavefunctions are called orbitals."},{"Start":"04:13.115 ","End":"04:15.470","Text":"We can write Psi the wavefunction,"},{"Start":"04:15.470 ","End":"04:16.880","Text":"which is a function of r,"},{"Start":"04:16.880 ","End":"04:20.690","Text":"Theta and Phi as 2 separate parts,"},{"Start":"04:20.690 ","End":"04:23.497","Text":"multiplication of 2 separate independent parts."},{"Start":"04:23.497 ","End":"04:27.260","Text":"R which is a function of small r,"},{"Start":"04:27.260 ","End":"04:30.440","Text":"that\u0027s the distance, times Y,"},{"Start":"04:30.440 ","End":"04:33.560","Text":"which is a function of Theta and Phi."},{"Start":"04:33.560 ","End":"04:36.935","Text":"Now, the equations are quite difficult to solve."},{"Start":"04:36.935 ","End":"04:39.845","Text":"The Schrodinger equation, you can separate it into"},{"Start":"04:39.845 ","End":"04:43.930","Text":"an equation for little r and equations for Theta and Phi,"},{"Start":"04:43.930 ","End":"04:48.109","Text":"that can even be separated into 2 equations for Theta and Phi."},{"Start":"04:48.109 ","End":"04:52.070","Text":"But we\u0027re not going to do that in this course."},{"Start":"04:52.070 ","End":"04:57.020","Text":"We\u0027re just going to give the expressions and explain how to understand them."},{"Start":"04:57.020 ","End":"05:02.345","Text":"Now, important thing to note is that since the problem is 3-dimensional,"},{"Start":"05:02.345 ","End":"05:04.865","Text":"there are 3 quantum numbers,"},{"Start":"05:04.865 ","End":"05:08.255","Text":"and we call them n, l and m_l."},{"Start":"05:08.255 ","End":"05:14.850","Text":"In the next video, we\u0027ll explain the meaning of these 3 quantum numbers."}],"ID":20937},{"Watched":false,"Name":"Wavefunction of H Atom 2","Duration":"8m 56s","ChapterTopicVideoID":20163,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20163.jpeg","UploadDate":"2019-07-10T23:31:25.7870000","DurationForVideoObject":"PT8M56S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:05.745","Text":"In this video, we\u0027ll talk about the 3 quantum numbers used for the hydrogen atom."},{"Start":"00:05.745 ","End":"00:09.375","Text":"The first quantum number is called the principal quantum number,"},{"Start":"00:09.375 ","End":"00:14.640","Text":"and it\u0027s labeled with the letter n. N is called the principal quantum number,"},{"Start":"00:14.640 ","End":"00:18.810","Text":"and all orbitals with the same volume of n have the same energy."},{"Start":"00:18.810 ","End":"00:23.115","Text":"We\u0027ll see in the next video that they\u0027re called degenerate orbitals."},{"Start":"00:23.115 ","End":"00:27.749","Text":"All orbitals with the same n are in the same shell."},{"Start":"00:27.749 ","End":"00:31.290","Text":"The volume of n defines the shell."},{"Start":"00:31.290 ","End":"00:34.680","Text":"Now n can take the values 1, 2, 3,"},{"Start":"00:34.680 ","End":"00:35.985","Text":"and so on,"},{"Start":"00:35.985 ","End":"00:39.220","Text":"just as the Bohr atom."},{"Start":"00:41.330 ","End":"00:46.760","Text":"As n increases, the electrons are further from the nucleus,"},{"Start":"00:46.760 ","End":"00:50.960","Text":"the orbitals and electrons are further from the nucleus."},{"Start":"00:50.960 ","End":"00:56.060","Text":"Now the second quantum number is called the orbital angular momentum quantum"},{"Start":"00:56.060 ","End":"01:02.060","Text":"number labeled l. L is called the orbital angular momentum quantum number,"},{"Start":"01:02.060 ","End":"01:05.795","Text":"and it\u0027s related to the motion of the electrons around the nucleus."},{"Start":"01:05.795 ","End":"01:11.105","Text":"All orbitals with the same volume of l are in the same subshell."},{"Start":"01:11.105 ","End":"01:14.000","Text":"Whereas n labeled the shell,"},{"Start":"01:14.000 ","End":"01:17.820","Text":"nl will label a subshell."},{"Start":"01:19.880 ","End":"01:23.010","Text":"L takes the values 0,"},{"Start":"01:23.010 ","End":"01:27.500","Text":"1, and so on until we get to n minus 1,"},{"Start":"01:27.500 ","End":"01:34.630","Text":"and the total number of subshells is n. We count the number from 0 to n minus 1,"},{"Start":"01:34.630 ","End":"01:40.385","Text":"we get n. Supposing n=3,"},{"Start":"01:40.385 ","End":"01:44.230","Text":"we\u0027ll have l=0,"},{"Start":"01:44.230 ","End":"01:47.005","Text":"1 and 2, 3 values."},{"Start":"01:47.005 ","End":"01:50.300","Text":"As l increases, the angular momentum,"},{"Start":"01:50.300 ","End":"01:53.128","Text":"most of the electron around the nucleus increases,"},{"Start":"01:53.128 ","End":"01:55.970","Text":"and the orbitals further from the nucleus."},{"Start":"01:55.970 ","End":"01:58.565","Text":"It\u0027s a bit like going round a bend,"},{"Start":"01:58.565 ","End":"02:03.320","Text":"the angular momentum depends on the speed with which we go round the bend."},{"Start":"02:03.320 ","End":"02:05.000","Text":"If you go faster,"},{"Start":"02:05.000 ","End":"02:07.340","Text":"your angular momentum will be greater,"},{"Start":"02:07.340 ","End":"02:11.645","Text":"and you might via up right to the side of the road."},{"Start":"02:11.645 ","End":"02:14.195","Text":"Whereas if you go slower,"},{"Start":"02:14.195 ","End":"02:17.270","Text":"your angular momentum will be smaller."},{"Start":"02:17.270 ","End":"02:22.190","Text":"Now, orbitals with 0 are called s orbitals,"},{"Start":"02:22.190 ","End":"02:27.530","Text":"and those with l=1 are called p orbitals,"},{"Start":"02:27.530 ","End":"02:32.995","Text":"and those with l=2 are called d orbitals,"},{"Start":"02:32.995 ","End":"02:37.895","Text":"and those with l=3 are called f orbitals."},{"Start":"02:37.895 ","End":"02:40.940","Text":"Now, these are historical names from"},{"Start":"02:40.940 ","End":"02:45.205","Text":"Tuskegee in which lines were distinguished as either sharp,"},{"Start":"02:45.205 ","End":"02:48.480","Text":"principal, diffuse, or fundamental."},{"Start":"02:48.480 ","End":"02:54.735","Text":"Let\u0027s take an example."},{"Start":"02:54.735 ","End":"02:59.110","Text":"If n=4, what are the possible values of l,"},{"Start":"02:59.110 ","End":"03:01.450","Text":"and what are the names of the subshells?"},{"Start":"03:01.450 ","End":"03:05.170","Text":"If n= 4,"},{"Start":"03:05.170 ","End":"03:06.375","Text":"l=0, 1,"},{"Start":"03:06.375 ","End":"03:11.760","Text":"2, 3 because 3 is 4 minus 1."},{"Start":"03:11.760 ","End":"03:14.295","Text":"Those are the values of l,"},{"Start":"03:14.295 ","End":"03:16.140","Text":"and how do we label them?"},{"Start":"03:16.140 ","End":"03:22.110","Text":"Well we label them 4s that\u0027s n=4,"},{"Start":"03:22.110 ","End":"03:23.675","Text":"l=0, 4p,"},{"Start":"03:23.675 ","End":"03:25.940","Text":"n=4, l=1,"},{"Start":"03:25.940 ","End":"03:29.480","Text":"4d that\u0027s l=2,"},{"Start":"03:29.480 ","End":"03:33.000","Text":"4f, that\u0027s l=3."},{"Start":"03:33.000 ","End":"03:35.205","Text":"These are our subshells."},{"Start":"03:35.205 ","End":"03:39.690","Text":"Now the third quantum number is the magnetic quantum number m_l."},{"Start":"03:39.690 ","End":"03:43.130","Text":"That\u0027s why we have a small m for magnetic."},{"Start":"03:43.130 ","End":"03:44.930","Text":"Third quantum number is m_l,"},{"Start":"03:44.930 ","End":"03:46.990","Text":"the magnetic quantum number."},{"Start":"03:46.990 ","End":"03:52.720","Text":"It takes the values minus l plus 1,"},{"Start":"03:52.720 ","End":"03:55.970","Text":"increasing up the ladder till we get to 0,"},{"Start":"03:55.970 ","End":"03:58.885","Text":"and then going into 1,"},{"Start":"03:58.885 ","End":"04:07.770","Text":"going up and up until we finally get to l. It steps between minus l steps,"},{"Start":"04:07.770 ","End":"04:11.640","Text":"step until we get 2l,"},{"Start":"04:11.640 ","End":"04:14.190","Text":"so minus l 2l."},{"Start":"04:14.190 ","End":"04:18.735","Text":"The number of values of m_l is 2l plus 1."},{"Start":"04:18.735 ","End":"04:20.430","Text":"Let\u0027s take an example."},{"Start":"04:20.430 ","End":"04:27.670","Text":"If l=1, then we\u0027ll have m_l will be minus 1,"},{"Start":"04:27.670 ","End":"04:32.180","Text":"0 and plus 1."},{"Start":"04:32.180 ","End":"04:35.445","Text":"That\u0027s 3 values, minus 1,"},{"Start":"04:35.445 ","End":"04:37.200","Text":"0, and plus 1."},{"Start":"04:37.200 ","End":"04:41.955","Text":"L is 1, that\u0027s the same as 2l plus 1 is also 3,"},{"Start":"04:41.955 ","End":"04:43.805","Text":"so we have 3 values."},{"Start":"04:43.805 ","End":"04:48.935","Text":"Now, we can explain this in the following way."},{"Start":"04:48.935 ","End":"04:51.770","Text":"Supposing we have an axis,"},{"Start":"04:51.770 ","End":"04:55.250","Text":"and l is pointing in a particular way."},{"Start":"04:55.250 ","End":"04:58.865","Text":"It can only point in 3 particular ways."},{"Start":"04:58.865 ","End":"05:06.555","Text":"One way where its projection on the axis is plus 1."},{"Start":"05:06.555 ","End":"05:12.242","Text":"One way, where its projection on the axis is 0,"},{"Start":"05:12.242 ","End":"05:18.230","Text":"and one way, where its projection on the axis is minus 1."},{"Start":"05:18.230 ","End":"05:20.285","Text":"So here are the 3 projections,"},{"Start":"05:20.285 ","End":"05:24.725","Text":"1, 0, and minus 1."},{"Start":"05:24.725 ","End":"05:27.125","Text":"In other words, m_l is quantized,"},{"Start":"05:27.125 ","End":"05:32.360","Text":"it can only have certain values and l is quantized."},{"Start":"05:32.360 ","End":"05:35.705","Text":"It can only point in certain directions."},{"Start":"05:35.705 ","End":"05:40.730","Text":"Now, orbitals, every allowed combination of n,"},{"Start":"05:40.730 ","End":"05:44.000","Text":"l, and m_l defines an orbital."},{"Start":"05:44.000 ","End":"05:47.900","Text":"It\u0027s like identity number."},{"Start":"05:47.900 ","End":"05:52.100","Text":"This is the identity number of the orbital n,"},{"Start":"05:52.100 ","End":"05:53.660","Text":"l, and m_l."},{"Start":"05:53.660 ","End":"05:55.430","Text":"That defines an orbital,"},{"Start":"05:55.430 ","End":"05:58.540","Text":"and the orbital is labeled n,"},{"Start":"05:58.540 ","End":"06:01.960","Text":"l and m_l as a subscript."},{"Start":"06:01.960 ","End":"06:04.065","Text":"Let\u0027s take an example."},{"Start":"06:04.065 ","End":"06:07.310","Text":"If n=4 and l=2,"},{"Start":"06:07.310 ","End":"06:09.845","Text":"what are the allowed values of m_l?"},{"Start":"06:09.845 ","End":"06:11.990","Text":"How many orbitals are there,"},{"Start":"06:11.990 ","End":"06:14.485","Text":"and what are the names of the orbitals?"},{"Start":"06:14.485 ","End":"06:19.335","Text":"If l=2, m_l is minus 2,"},{"Start":"06:19.335 ","End":"06:23.325","Text":"that\u0027s minus l minus 1,"},{"Start":"06:23.325 ","End":"06:25.645","Text":"0, 1, and 2."},{"Start":"06:25.645 ","End":"06:27.845","Text":"How many orbitals are there?"},{"Start":"06:27.845 ","End":"06:30.380","Text":"2l plus 1=5."},{"Start":"06:30.380 ","End":"06:34.600","Text":"So we can either do it from the formula 2l plus 1=5,"},{"Start":"06:34.600 ","End":"06:38.420","Text":"because l=2, or we can write them out,"},{"Start":"06:38.420 ","End":"06:40.025","Text":"and sum them up,"},{"Start":"06:40.025 ","End":"06:42.890","Text":"1, 2, 3, 4, 5."},{"Start":"06:42.890 ","End":"06:48.440","Text":"Now the names of the orbitals are 4d minus 2,"},{"Start":"06:48.440 ","End":"06:50.800","Text":"4d_minus 1, 4d_0,"},{"Start":"06:50.800 ","End":"06:54.685","Text":"4d_ plus 1, and 4d_plus 2."},{"Start":"06:54.685 ","End":"06:57.075","Text":"Here are the 5 orbitals."},{"Start":"06:57.075 ","End":"07:05.390","Text":"Now, these names are used by physicists or chemists interested in magnetic fields."},{"Start":"07:05.390 ","End":"07:09.470","Text":"But in generally when they\u0027re describing orbitals,"},{"Start":"07:09.470 ","End":"07:11.405","Text":"we use another notation,"},{"Start":"07:11.405 ","End":"07:13.480","Text":"one loved by chemists."},{"Start":"07:13.480 ","End":"07:16.790","Text":"Chemists usually use combination of orbitals with"},{"Start":"07:16.790 ","End":"07:21.590","Text":"the same values of n and l rather than the orbitals themselves."},{"Start":"07:21.590 ","End":"07:24.530","Text":"The reason for this is actually mathematical."},{"Start":"07:24.530 ","End":"07:27.335","Text":"Those of you who have learned about complex numbers,"},{"Start":"07:27.335 ","End":"07:29.870","Text":"will discover that these orbitals,"},{"Start":"07:29.870 ","End":"07:35.800","Text":"as you physicists like are complex."},{"Start":"07:35.800 ","End":"07:38.150","Text":"You can\u0027t draw them easily."},{"Start":"07:38.150 ","End":"07:42.350","Text":"Whereas chemists like something that\u0027s real and easy to draw,"},{"Start":"07:42.350 ","End":"07:44.390","Text":"so that\u0027s why they do this."},{"Start":"07:44.390 ","End":"07:46.205","Text":"Let\u0027s take an example."},{"Start":"07:46.205 ","End":"07:48.275","Text":"For example, p_0,"},{"Start":"07:48.275 ","End":"07:55.515","Text":"that\u0027s l=1, m_l=0."},{"Start":"07:55.515 ","End":"08:01.185","Text":"Chemists write as p_z because it points in the z direction."},{"Start":"08:01.185 ","End":"08:09.205","Text":"They take combinations of p_plus 1 and p_minus 1 and then they get p_x and p_y."},{"Start":"08:09.205 ","End":"08:11.695","Text":"We have 2 combinations,"},{"Start":"08:11.695 ","End":"08:17.430","Text":"p_plus 1 plus p_minus 1."},{"Start":"08:17.430 ","End":"08:22.290","Text":"Another one p_plus 1 minus p_minus 1."},{"Start":"08:22.290 ","End":"08:26.360","Text":"One points in the x direction and one in the y-direction,"},{"Start":"08:26.360 ","End":"08:29.435","Text":"and they\u0027re called p_x and p_y."},{"Start":"08:29.435 ","End":"08:33.455","Text":"We have p_z, p_x,"},{"Start":"08:33.455 ","End":"08:37.875","Text":"and p_y and then in later video,"},{"Start":"08:37.875 ","End":"08:42.830","Text":"we\u0027ll draw these and see that they point along the x,"},{"Start":"08:42.830 ","End":"08:45.470","Text":"y, and z axis."},{"Start":"08:45.470 ","End":"08:51.165","Text":"In this video, we\u0027ve talked about the wave functions of a hydrogen-like species,"},{"Start":"08:51.165 ","End":"08:56.679","Text":"and in particular we discussed the quantum numbers."}],"ID":20938},{"Watched":false,"Name":"Energy Levels of H Atom","Duration":"3m 36s","ChapterTopicVideoID":20164,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20164.jpeg","UploadDate":"2019-07-10T23:32:36.9530000","DurationForVideoObject":"PT3M36S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.390","Text":"In this video, we\u0027ll talk about the energy levels of"},{"Start":"00:03.390 ","End":"00:07.860","Text":"the hydrogen atom that are obtained from the Schrodinger equation."},{"Start":"00:07.860 ","End":"00:12.570","Text":"Once again, we\u0027re talking about energy levels of hydrogen-like species."},{"Start":"00:12.570 ","End":"00:14.310","Text":"That\u0027s Hydrogen, Helium plus,"},{"Start":"00:14.310 ","End":"00:19.060","Text":"Lithium 2 plus anything that has 1 electron."},{"Start":"00:20.660 ","End":"00:23.990","Text":"We saw in a previous video that the electron is"},{"Start":"00:23.990 ","End":"00:27.305","Text":"confined by its attraction to the nucleus,"},{"Start":"00:27.305 ","End":"00:29.690","Text":"the energy is quantized."},{"Start":"00:29.690 ","End":"00:33.320","Text":"It turns out that the energy levels calculated from"},{"Start":"00:33.320 ","End":"00:37.975","Text":"Schrodinger equation are identical to those of the Bohr model."},{"Start":"00:37.975 ","End":"00:44.165","Text":"En = minus R h squared divided by n squared,"},{"Start":"00:44.165 ","End":"00:46.985","Text":"where RH is the Rydberg constant,"},{"Start":"00:46.985 ","End":"00:51.340","Text":"2.179 times 10^_18 Joules,"},{"Start":"00:51.340 ","End":"00:52.865","Text":"Z, of course,"},{"Start":"00:52.865 ","End":"01:01.845","Text":"is the atomic number and n is an index that goes from n=1,2 and so on,"},{"Start":"01:01.845 ","End":"01:04.370","Text":"it\u0027s a principle quantum number."},{"Start":"01:04.370 ","End":"01:08.270","Text":"Now, as I said in the previous video,"},{"Start":"01:08.270 ","End":"01:15.050","Text":"all the orbitals with the same value of n are degenerate."},{"Start":"01:15.050 ","End":"01:21.455","Text":"All the orbitals in the same shell have the same energy and are degenerate."},{"Start":"01:21.455 ","End":"01:23.270","Text":"Here\u0027s an example,"},{"Start":"01:23.270 ","End":"01:28.870","Text":"how many degenerate orbitals are there in the n = 3 shell?"},{"Start":"01:28.870 ","End":"01:33.650","Text":"Let\u0027s start with what are the values of l?"},{"Start":"01:33.650 ","End":"01:35.480","Text":"If n = 3,"},{"Start":"01:35.480 ","End":"01:39.770","Text":"recall the l = 0,1 and 2."},{"Start":"01:39.770 ","End":"01:42.345","Text":"If l = 0,"},{"Start":"01:42.345 ","End":"01:47.110","Text":"that\u0027s the (3s) orbitals, the 3s subshell."},{"Start":"01:47.110 ","End":"01:51.695","Text":"Then the number of orbitals is 2 times l plus 1,"},{"Start":"01:51.695 ","End":"01:56.254","Text":"it\u0027s 2 times 0 plus 1,1 single orbital."},{"Start":"01:56.254 ","End":"02:01.075","Text":"There\u0027s only 1 orbital in the 3s subshell,"},{"Start":"02:01.075 ","End":"02:03.045","Text":"l equal to 1,"},{"Start":"02:03.045 ","End":"02:05.284","Text":"that\u0027s a 3p subshell."},{"Start":"02:05.284 ","End":"02:06.935","Text":"How many orbitals are there?"},{"Start":"02:06.935 ","End":"02:08.210","Text":"2 times 1,"},{"Start":"02:08.210 ","End":"02:11.995","Text":"l is equal to 1 plus 1, that\u0027s 3 orbitals."},{"Start":"02:11.995 ","End":"02:14.070","Text":"When n is equal to 2,"},{"Start":"02:14.070 ","End":"02:16.365","Text":"that\u0027s the 3d subshell,"},{"Start":"02:16.365 ","End":"02:17.970","Text":"we have 2 times 2,"},{"Start":"02:17.970 ","End":"02:20.235","Text":"l is equal to 2 plus 1,"},{"Start":"02:20.235 ","End":"02:22.395","Text":"there are 5 orbitals,"},{"Start":"02:22.395 ","End":"02:30.470","Text":"the total is 1 plus 3 plus 5 equal to 9."},{"Start":"02:30.470 ","End":"02:34.535","Text":"We have 9 orbitals which are degenerate."},{"Start":"02:34.535 ","End":"02:41.280","Text":"9 is equal to 3^2 and the general expression is n^2."},{"Start":"02:43.670 ","End":"02:47.310","Text":"We can conclude the 3s, 3p,"},{"Start":"02:47.310 ","End":"02:49.905","Text":"and 3d orbitals,"},{"Start":"02:49.905 ","End":"02:55.190","Text":"all those orbitals have the same energy and are degenerate."},{"Start":"02:55.190 ","End":"02:57.385","Text":"Another case, for example,"},{"Start":"02:57.385 ","End":"03:01.695","Text":"are the 4 orbitals where n equals 2,"},{"Start":"03:01.695 ","End":"03:03.150","Text":"the n is equal to,"},{"Start":"03:03.150 ","End":"03:06.420","Text":"we have 1s orbital and 3p orbitals,"},{"Start":"03:06.420 ","End":"03:12.075","Text":"a total of 4. n is equal to 2,"},{"Start":"03:12.075 ","End":"03:18.525","Text":"this is n^2, 2^2."},{"Start":"03:18.525 ","End":"03:20.310","Text":"There\u0027s our general expression,"},{"Start":"03:20.310 ","End":"03:28.260","Text":"the total number of degenerate orbitals in a particular shell is n^2."},{"Start":"03:28.260 ","End":"03:33.785","Text":"In this video, we talked about the energy levels of hydrogen-like species,"},{"Start":"03:33.785 ","End":"03:36.750","Text":"atoms, or ions."}],"ID":20939},{"Watched":false,"Name":"Exercise 1","Duration":"1m 7s","ChapterTopicVideoID":22939,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22939.jpeg","UploadDate":"2020-12-18T04:17:56.0770000","DurationForVideoObject":"PT1M7S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.864","Text":"Hi. We\u0027re going to solve the following exercise."},{"Start":"00:02.864 ","End":"00:08.130","Text":"Calculate the energy in joule corresponding to n=7 in a hydrogen atom."},{"Start":"00:08.130 ","End":"00:11.310","Text":"We want to find the energy of the 7th level."},{"Start":"00:11.310 ","End":"00:16.620","Text":"The energy of a certain level equals minus R_H,"},{"Start":"00:16.620 ","End":"00:19.935","Text":"which is the Rydberg constant,"},{"Start":"00:19.935 ","End":"00:25.710","Text":"divided by n^2 and n is the level of the energy."},{"Start":"00:25.710 ","End":"00:28.410","Text":"In our case we have n=7,"},{"Start":"00:28.410 ","End":"00:31.170","Text":"so we\u0027re just going to E_7,"},{"Start":"00:31.170 ","End":"00:34.140","Text":"which is the energy of the 7th that will equals minus,"},{"Start":"00:34.140 ","End":"00:41.890","Text":"R_H is 2.179 times 10 to the negative 18 joule."},{"Start":"00:42.200 ","End":"00:46.020","Text":"All of this is divided by n^2."},{"Start":"00:46.020 ","End":"00:47.850","Text":"Again, n=7,"},{"Start":"00:47.850 ","End":"00:50.330","Text":"so divided by 7^2."},{"Start":"00:50.330 ","End":"00:58.925","Text":"This gives us minus 4.45 times 10^negative 20 joule."},{"Start":"00:58.925 ","End":"01:04.715","Text":"Your final answer is minus 4.45 times 10^negative 20 joule."},{"Start":"01:04.715 ","End":"01:07.680","Text":"Thank you very much for watching."}],"ID":23764},{"Watched":false,"Name":"Exercise 2","Duration":"3m 12s","ChapterTopicVideoID":22940,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22940.jpeg","UploadDate":"2020-12-18T04:18:14.2300000","DurationForVideoObject":"PT3M12S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.849","Text":"Hi, We\u0027re going to solve the following exercise."},{"Start":"00:02.849 ","End":"00:06.390","Text":"A, calculate the energy loss Delta E when an electron in"},{"Start":"00:06.390 ","End":"00:11.655","Text":"a hydrogen atom undergoes a transition from n=4 to n=2."},{"Start":"00:11.655 ","End":"00:14.895","Text":"B, calculate the frequency of the emitted photon."},{"Start":"00:14.895 ","End":"00:17.160","Text":"In a, we have to calculate the energy"},{"Start":"00:17.160 ","End":"00:21.015","Text":"lost when an electron undergoes a certain transition."},{"Start":"00:21.015 ","End":"00:23.715","Text":"We\u0027re going to use the equation Delta E,"},{"Start":"00:23.715 ","End":"00:29.140","Text":"the difference in the energy equals minus R_H,"},{"Start":"00:29.180 ","End":"00:33.690","Text":"R_H is the Rydberg constant times 1 divided by"},{"Start":"00:33.690 ","End":"00:39.370","Text":"the final level squared minus 1 divided by the initial level squared."},{"Start":"00:39.950 ","End":"00:46.050","Text":"In our case, Delta E equals again minus the Rydberg constant,"},{"Start":"00:46.050 ","End":"00:50.250","Text":"so it\u0027s minus 2.179 times"},{"Start":"00:50.250 ","End":"00:59.070","Text":"10^negative 18 joule times 1 divided by the final level squared."},{"Start":"00:59.070 ","End":"01:01.770","Text":"The final level is n=2,"},{"Start":"01:01.770 ","End":"01:07.310","Text":"so 1 divided by 2^2 minus 1 divided by the initial level squared."},{"Start":"01:07.310 ","End":"01:11.125","Text":"Meaning 1 divided by 4^2."},{"Start":"01:11.125 ","End":"01:21.210","Text":"This equals minus 4.09 times 10^negative 19 joule."},{"Start":"01:21.210 ","End":"01:22.860","Text":"That\u0027s our answer for a,"},{"Start":"01:22.860 ","End":"01:25.520","Text":"that\u0027s the Delta energy that we found."},{"Start":"01:25.520 ","End":"01:30.935","Text":"Now I just want to comment that this energy is negative since the energy here is lost,"},{"Start":"01:30.935 ","End":"01:32.570","Text":"the energy is emitted."},{"Start":"01:32.570 ","End":"01:36.365","Text":"Now in b, we have to calculate the frequency of the emitted photon."},{"Start":"01:36.365 ","End":"01:41.700","Text":"First of all, the energy of the photon equals the"},{"Start":"01:41.700 ","End":"01:47.240","Text":"Delta E. The difference in the energy which is emitted."},{"Start":"01:47.240 ","End":"01:51.530","Text":"However, we take the positive value"},{"Start":"01:51.530 ","End":"01:55.775","Text":"of this energy since now we\u0027re talking about the photon."},{"Start":"01:55.775 ","End":"02:00.810","Text":"The energy of the photon also equals h_Mu."},{"Start":"02:00.920 ","End":"02:07.430","Text":"H is Planck\u0027s constant and Mu is the frequency and we\u0027re looking for the frequency."},{"Start":"02:07.430 ","End":"02:11.180","Text":"Therefore, we\u0027re going to use Mu equals the energy of"},{"Start":"02:11.180 ","End":"02:16.730","Text":"the photon divided by Planck\u0027s constant."},{"Start":"02:16.730 ","End":"02:20.045","Text":"Again, the energy of the photon is what we found in a,"},{"Start":"02:20.045 ","End":"02:22.400","Text":"however, it\u0027s the positive value of what we found in a,"},{"Start":"02:22.400 ","End":"02:28.715","Text":"so it\u0027s 4.09 times 10^negative 19 joule,"},{"Start":"02:28.715 ","End":"02:31.010","Text":"going to divide this by Planck\u0027s constant,"},{"Start":"02:31.010 ","End":"02:40.690","Text":"which is 6.626 times 10^negative 34 joule times second."},{"Start":"02:40.690 ","End":"02:43.425","Text":"Joules will cancel out."},{"Start":"02:43.425 ","End":"02:52.589","Text":"This equals 6.17 times 10^14th, inverse seconds."},{"Start":"02:52.589 ","End":"02:56.570","Text":"Since it\u0027s 1 divided by S is the same as S minus 1"},{"Start":"02:56.570 ","End":"03:01.120","Text":"inverse second to the frequency that we found for the emitted photon."},{"Start":"03:01.120 ","End":"03:07.895","Text":"Mu equals 6.17 times 10^14th inverse seconds."},{"Start":"03:07.895 ","End":"03:10.145","Text":"That is our final answer for b."},{"Start":"03:10.145 ","End":"03:12.720","Text":"Thank you very much for listening."}],"ID":23765},{"Watched":false,"Name":"Exercise 3","Duration":"4m 30s","ChapterTopicVideoID":22941,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22941.jpeg","UploadDate":"2020-12-18T04:18:32.6030000","DurationForVideoObject":"PT4M30S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.685","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:02.685 ","End":"00:05.910","Text":"Calculate the frequency in hertz and wavelength in nanometers of"},{"Start":"00:05.910 ","End":"00:10.095","Text":"a photon emitted as a result of an electron transition from n=7,"},{"Start":"00:10.095 ","End":"00:12.345","Text":"to n=3 in a hydrogen atom."},{"Start":"00:12.345 ","End":"00:14.730","Text":"We have a transition again from n=7,"},{"Start":"00:14.730 ","End":"00:19.770","Text":"to n=3, and we want to calculate the frequency and the wavelength of the photon emitted."},{"Start":"00:19.770 ","End":"00:25.575","Text":"Now we know that the energy of the photon equals h Mu,"},{"Start":"00:25.575 ","End":"00:32.040","Text":"and we also know that the difference in energy between the levels equals minus RH,"},{"Start":"00:32.040 ","End":"00:34.470","Text":"which is derived with constant times 1 divided by"},{"Start":"00:34.470 ","End":"00:39.015","Text":"the final level squared minus 1 divided by the initial level squared."},{"Start":"00:39.015 ","End":"00:42.570","Text":"Now since we\u0027re interested in the photon\u0027s energy,"},{"Start":"00:42.570 ","End":"00:47.210","Text":"the energy of a photon is the positive value of"},{"Start":"00:47.210 ","End":"00:51.770","Text":"Delta E. Now we\u0027re"},{"Start":"00:51.770 ","End":"00:53.330","Text":"going to look at the frequency because we want"},{"Start":"00:53.330 ","End":"00:56.435","Text":"to calculate the frequency of the emitted photon."},{"Start":"00:56.435 ","End":"01:01.550","Text":"The frequency, I\u0027m just going to divide both sides by Planck\u0027s constant,"},{"Start":"01:01.550 ","End":"01:07.310","Text":"equals the energy of the photon divided by Planck\u0027s constant,"},{"Start":"01:07.310 ","End":"01:13.250","Text":"which is h. The energy of the photon also equals the positive value of Delta E,"},{"Start":"01:13.250 ","End":"01:16.520","Text":"meaning equals R_H,"},{"Start":"01:16.520 ","End":"01:20.510","Text":"the Rydberg constant times 1 divided by the final level"},{"Start":"01:20.510 ","End":"01:25.415","Text":"squared minus 1 divided by the initial level squared."},{"Start":"01:25.415 ","End":"01:27.440","Text":"And all of this, as you can see,"},{"Start":"01:27.440 ","End":"01:30.055","Text":"we have to divide by Planck\u0027s constant."},{"Start":"01:30.055 ","End":"01:33.680","Text":"So Mu, the frequency equals RH,"},{"Start":"01:33.680 ","End":"01:34.880","Text":"which is the Rydberg constant,"},{"Start":"01:34.880 ","End":"01:37.115","Text":"divided by h which is Planck\u0027s constant,"},{"Start":"01:37.115 ","End":"01:42.200","Text":"times 1 divided by the final level squared minus 1 divided by the initial level squared."},{"Start":"01:42.200 ","End":"01:48.200","Text":"This equals, the Rydberg where constant is 2.179 times"},{"Start":"01:48.200 ","End":"01:54.200","Text":"10^negative 18 joule divided by Planck\u0027s constant,"},{"Start":"01:54.200 ","End":"02:01.595","Text":"which is 6.626 times 10^negative 34 joules times second."},{"Start":"02:01.595 ","End":"02:03.245","Text":"Joules cancel out."},{"Start":"02:03.245 ","End":"02:07.925","Text":"All of this is times 1 divided by the final level, which is 3."},{"Start":"02:07.925 ","End":"02:13.100","Text":"This is 3 squared minus 1 divided by the initial level squared,"},{"Start":"02:13.100 ","End":"02:15.350","Text":"which is 7, so 7 squared."},{"Start":"02:15.350 ","End":"02:21.610","Text":"This equals 2.98 times 10^14,"},{"Start":"02:21.610 ","End":"02:24.995","Text":"and we\u0027re left with inverse second."},{"Start":"02:24.995 ","End":"02:29.070","Text":"That is the frequency of the emitted photon."},{"Start":"02:29.260 ","End":"02:33.080","Text":"That\u0027s the frequency of the emitted photon in inverse second."},{"Start":"02:33.080 ","End":"02:35.120","Text":"An inverse second also equals hertz,"},{"Start":"02:35.120 ","End":"02:40.920","Text":"so this also equals to 2.98 times 10^14 hertz."},{"Start":"02:43.700 ","End":"02:47.780","Text":"Now we\u0027re asked to find the wavelength of this emitted photon."},{"Start":"02:47.780 ","End":"02:52.550","Text":"For this purpose, we\u0027re going to use the equation C equals Lambda Mu."},{"Start":"02:52.550 ","End":"02:55.565","Text":"C is the speed of light constant,"},{"Start":"02:55.565 ","End":"02:57.050","Text":"Lambda is the wavelength,"},{"Start":"02:57.050 ","End":"02:58.355","Text":"and Mu is the frequency."},{"Start":"02:58.355 ","End":"03:00.665","Text":"Now we know Mu and we have to find Lambda."},{"Start":"03:00.665 ","End":"03:04.325","Text":"We\u0027re going to divide both sides by Mu, by the frequency."},{"Start":"03:04.325 ","End":"03:10.540","Text":"That\u0027s going to give us Lambda equals C divided by Mu."},{"Start":"03:10.910 ","End":"03:17.930","Text":"C again is the speed of light constant that equals 3 times 10^8 meters per second,"},{"Start":"03:17.930 ","End":"03:20.060","Text":"divided by Mu,"},{"Start":"03:20.060 ","End":"03:23.810","Text":"which is the frequency which we found in a,"},{"Start":"03:23.810 ","End":"03:32.440","Text":"which equals 2.98 times 10^14 inverse second."},{"Start":"03:32.440 ","End":"03:40.245","Text":"After dividing, we get 1.01 times 10^negative 6 meters."},{"Start":"03:40.245 ","End":"03:42.875","Text":"I want you to take a quick look at the units."},{"Start":"03:42.875 ","End":"03:44.560","Text":"We have meters per second,"},{"Start":"03:44.560 ","End":"03:49.250","Text":"so meters per second divided by inverse second,"},{"Start":"03:49.250 ","End":"03:53.000","Text":"which is 1 divided by S. When you have a fraction divided by the fraction,"},{"Start":"03:53.000 ","End":"03:56.330","Text":"you multiply the numerator and the denominator,"},{"Start":"03:56.330 ","End":"03:58.400","Text":"and you multiply it again,"},{"Start":"03:58.400 ","End":"04:00.010","Text":"the numerator and the denominator."},{"Start":"04:00.010 ","End":"04:03.505","Text":"This equals, if we look meters times second,"},{"Start":"04:03.505 ","End":"04:07.295","Text":"divided by second times 1, which is seconds."},{"Start":"04:07.295 ","End":"04:10.695","Text":"The seconds cancel out and we\u0027re left with meters."},{"Start":"04:10.695 ","End":"04:13.785","Text":"Our units are meters."},{"Start":"04:13.785 ","End":"04:16.560","Text":"This 10^negative 6 is micro,"},{"Start":"04:16.560 ","End":"04:20.200","Text":"so it equals 1.01 micrometer."},{"Start":"04:20.200 ","End":"04:24.410","Text":"The wavelength that we found equals 1.01 micrometer,"},{"Start":"04:24.410 ","End":"04:26.660","Text":"the wavelength of the emitted photon."},{"Start":"04:26.660 ","End":"04:28.220","Text":"That is our final answer."},{"Start":"04:28.220 ","End":"04:30.750","Text":"Thank you very much for watching."}],"ID":23766},{"Watched":false,"Name":"Exercise 4","Duration":"3m 24s","ChapterTopicVideoID":22942,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22942.jpeg","UploadDate":"2020-12-18T04:18:46.2370000","DurationForVideoObject":"PT3M24S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.550","Text":"Hi, We\u0027re going to solve the following exercise."},{"Start":"00:02.550 ","End":"00:06.480","Text":"A photon of wavelength 2.63 micrometers is emitted from"},{"Start":"00:06.480 ","End":"00:11.835","Text":"a hydrogen atom as a result of an electron transition from n equals 6 to n final,"},{"Start":"00:11.835 ","End":"00:14.520","Text":"find the final level."},{"Start":"00:14.520 ","End":"00:24.240","Text":"We know that the energy of the photon equals hu and this equals hc divided by Lambda."},{"Start":"00:24.240 ","End":"00:29.220","Text":"We also know that the Delta energy of a transition in a hydrogen atom,"},{"Start":"00:29.220 ","End":"00:34.050","Text":"that Delta energy equals minus R_H,"},{"Start":"00:34.050 ","End":"00:36.600","Text":"which is the Rydberg constant times 1 divided by"},{"Start":"00:36.600 ","End":"00:42.150","Text":"the final level minus 1 divided by the initial level."},{"Start":"00:42.150 ","End":"00:51.320","Text":"The energy of the photon which is emitted equals Delta energy of the transition in value,"},{"Start":"00:51.320 ","End":"00:55.980","Text":"however, it is the positive value."},{"Start":"00:57.650 ","End":"01:06.610","Text":"Again, the energy of the photon equals hc divided by Lambda,"},{"Start":"01:06.670 ","End":"01:10.160","Text":"which equals the positive of Delta E,"},{"Start":"01:10.160 ","End":"01:13.970","Text":"meaning equals the Rydberg constant times 1 divided"},{"Start":"01:13.970 ","End":"01:19.440","Text":"by the final level minus 1 divided by the initial."},{"Start":"01:19.970 ","End":"01:25.447","Text":"Again, the energy of the photon equals hc divided by Lambda h is the Planck constant,"},{"Start":"01:25.447 ","End":"01:33.170","Text":"so that\u0027s 6.626 times 10^-34 joules times second."},{"Start":"01:33.170 ","End":"01:34.820","Text":"This is multiplied by c,"},{"Start":"01:34.820 ","End":"01:36.697","Text":"which is the speed of light constant,"},{"Start":"01:36.697 ","End":"01:40.400","Text":"so it\u0027s 3 times 10^8 meters per second."},{"Start":"01:40.400 ","End":"01:43.460","Text":"We can already see that the seconds cancel out here."},{"Start":"01:43.460 ","End":"01:47.190","Text":"And all of this is divided by Lambda."},{"Start":"01:47.920 ","End":"01:53.280","Text":"Lambda is the wavelength which is 2.63 micrometers."},{"Start":"01:54.730 ","End":"01:59.300","Text":"Then we\u0027re just going to multiply by a conversion factor already in order to convert"},{"Start":"01:59.300 ","End":"02:03.665","Text":"the micrometers into meters so it will be more comfortable for us with the units."},{"Start":"02:03.665 ","End":"02:08.340","Text":"In 1 meter, we have 10^6 micro meters,"},{"Start":"02:08.340 ","End":"02:09.785","Text":"micro meters cancel out."},{"Start":"02:09.785 ","End":"02:11.690","Text":"All of this equals R_H,"},{"Start":"02:11.690 ","End":"02:13.820","Text":"which is the Rydberg constant,"},{"Start":"02:13.820 ","End":"02:20.045","Text":"which is 2.179 times 10^-18 joule."},{"Start":"02:20.045 ","End":"02:23.675","Text":"This is multiplied by 1 divided by the final level,"},{"Start":"02:23.675 ","End":"02:25.700","Text":"which is actually what we need to find."},{"Start":"02:25.700 ","End":"02:31.220","Text":"So 1 divided by n_f squared minus 1 divided by the initial level squared,"},{"Start":"02:31.220 ","End":"02:35.040","Text":"which equals 6, so 1 divided by 6^2."},{"Start":"02:35.200 ","End":"02:38.990","Text":"If we look at the units, we can also see that the joules cancel out."},{"Start":"02:38.990 ","End":"02:42.680","Text":"We have joules on both sides and the meters also cancel out too."},{"Start":"02:42.680 ","End":"02:49.555","Text":"After solving this, we get 1 divided by the final level squared equals"},{"Start":"02:49.555 ","End":"03:00.030","Text":"0.062 the final level squared equals 1 divided by 0.062,"},{"Start":"03:01.630 ","End":"03:09.600","Text":"which equals 16.13. n_f comes to 4."},{"Start":"03:09.600 ","End":"03:13.040","Text":"Since n_f squared equals approximately 16."},{"Start":"03:13.040 ","End":"03:16.490","Text":"The final level that we found for"},{"Start":"03:16.490 ","End":"03:20.750","Text":"the transition of the electron in the hydrogen atom equals 4."},{"Start":"03:20.750 ","End":"03:22.160","Text":"That is our final answer."},{"Start":"03:22.160 ","End":"03:24.660","Text":"Thank you very much for watching."}],"ID":23767},{"Watched":false,"Name":"Exercise 5","Duration":"3m 59s","ChapterTopicVideoID":22943,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22943.jpeg","UploadDate":"2020-12-18T04:19:04.3300000","DurationForVideoObject":"PT3M59S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.564","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:02.564 ","End":"00:06.975","Text":"The radius of n=n^2 times the Bohr radius,"},{"Start":"00:06.975 ","End":"00:09.600","Text":"and the Bohr radius=0.53 angstrom."},{"Start":"00:09.600 ","End":"00:15.315","Text":"A, calculate the radius for the Bohr hydrogen atom corresponding to n=3."},{"Start":"00:15.315 ","End":"00:19.515","Text":"B, the radius of n=2.12 angstrom,"},{"Start":"00:19.515 ","End":"00:21.180","Text":"calculate n, and c,"},{"Start":"00:21.180 ","End":"00:24.390","Text":"calculate the increase in distance from the nucleus when an electron is"},{"Start":"00:24.390 ","End":"00:28.155","Text":"excited from the second to the third orbit in a Bohr hydrogen atom."},{"Start":"00:28.155 ","End":"00:30.410","Text":"We\u0027re going to start with a, in a we need to calculate"},{"Start":"00:30.410 ","End":"00:34.395","Text":"the Bohr radius when the quantum number equals 3."},{"Start":"00:34.395 ","End":"00:37.490","Text":"Here we\u0027re given the equation to calculate the Bohr radius."},{"Start":"00:37.490 ","End":"00:41.090","Text":"So r_n of a certain quantum number equals that quantum number"},{"Start":"00:41.090 ","End":"00:45.485","Text":"squared times the Bohr radius and we\u0027re given the value of the Bohr radius."},{"Start":"00:45.485 ","End":"00:49.520","Text":"In our case in a, we\u0027re given that n=3,"},{"Start":"00:49.520 ","End":"00:53.070","Text":"so the radius of n equals 3,"},{"Start":"00:53.070 ","End":"00:57.960","Text":"equals 3^2 because it\u0027s n^2 times the Bohr radius,"},{"Start":"00:57.960 ","End":"00:59.970","Text":"which is 0.53 angstroms,"},{"Start":"00:59.970 ","End":"01:03.900","Text":"so times 0.53 angstroms."},{"Start":"01:03.900 ","End":"01:07.680","Text":"This equals 4.77 angstrom,"},{"Start":"01:07.680 ","End":"01:10.810","Text":"and that is our answer for a."},{"Start":"01:12.380 ","End":"01:14.545","Text":"Just a quick reminder,"},{"Start":"01:14.545 ","End":"01:18.425","Text":"angstrom equals 10 to the negative 10 meters."},{"Start":"01:18.425 ","End":"01:21.550","Text":"Now in b, we need to calculate n,"},{"Start":"01:21.550 ","End":"01:26.455","Text":"the quantum number when we know that the radius equals 2.12 angstrom."},{"Start":"01:26.455 ","End":"01:29.635","Text":"We want to calculate n. Again,"},{"Start":"01:29.635 ","End":"01:34.930","Text":"the equation that we\u0027re using is r_n the radius at a certain quantum number equals"},{"Start":"01:34.930 ","End":"01:42.279","Text":"n^2 times the Bohr radius and the Bohr radius equals 0.53 angstrom."},{"Start":"01:42.279 ","End":"01:43.960","Text":"Now we want to calculate n,"},{"Start":"01:43.960 ","End":"01:46.735","Text":"so we\u0027re just going to divide both sides by the Bohr radius,"},{"Start":"01:46.735 ","End":"01:56.150","Text":"so n^2 equals the radius at a certain quantum number divided by the Bohr radius,"},{"Start":"01:56.150 ","End":"02:01.140","Text":"and this equals, r_n=2.12 angstrom."},{"Start":"02:02.410 ","End":"02:05.990","Text":"The Bohr radius is 0.53 angstrom."},{"Start":"02:05.990 ","End":"02:08.180","Text":"We can see that our angstroms cancel out,"},{"Start":"02:08.180 ","End":"02:16.865","Text":"so n^2=4, n=2,"},{"Start":"02:16.865 ","End":"02:19.925","Text":"so our answer for b is that n=2."},{"Start":"02:19.925 ","End":"02:21.815","Text":"Now let\u0027s go on to c,"},{"Start":"02:21.815 ","End":"02:25.970","Text":"and c we have to calculate the increase in distance from the nucleus when"},{"Start":"02:25.970 ","End":"02:30.815","Text":"an electron is excited from the second to the third orbit in a Bohr hydrogen atom."},{"Start":"02:30.815 ","End":"02:34.725","Text":"In b, we can see n=2 meaning we\u0027re talking about"},{"Start":"02:34.725 ","End":"02:41.100","Text":"this second orbit and we know that the radius that was given is 2.12 angstrom."},{"Start":"02:41.100 ","End":"02:43.515","Text":"We know that when n=2,"},{"Start":"02:43.515 ","End":"02:50.775","Text":"the radius of 2 actually equals 2.12 angstrom. We know this from b."},{"Start":"02:50.775 ","End":"02:54.145","Text":"Now from a, we know that when n equals 3,"},{"Start":"02:54.145 ","End":"03:02.200","Text":"the radius that we calculated equals 4.77 angstrom."},{"Start":"03:02.200 ","End":"03:05.300","Text":"Now we want to calculate the increase in distance from"},{"Start":"03:05.300 ","End":"03:10.160","Text":"the nucleus when an electron is excited from the second to the third orbit,"},{"Start":"03:10.160 ","End":"03:13.360","Text":"meaning the electron goes from the second orbit,"},{"Start":"03:13.360 ","End":"03:20.120","Text":"which the radius is 2.12 angstrom to the third orbit which the radius is 4.77 angstrom."},{"Start":"03:20.120 ","End":"03:23.030","Text":"We\u0027re asked to find the increase in the distance."},{"Start":"03:23.030 ","End":"03:31.365","Text":"So the increase is the difference between that radius when n=3 to the radius when n=2."},{"Start":"03:31.365 ","End":"03:32.660","Text":"The difference in distance,"},{"Start":"03:32.660 ","End":"03:37.835","Text":"we\u0027re just going to call this d equals r_3 minus r_2,"},{"Start":"03:37.835 ","End":"03:45.525","Text":"and that equals 4.77 angstrom minus 2.12 angstrom,"},{"Start":"03:45.525 ","End":"03:49.180","Text":"and this equals 2.65 angstrom."},{"Start":"03:49.180 ","End":"03:55.715","Text":"Our answer for c is that the distance equals 2.65 angstrom."},{"Start":"03:55.715 ","End":"03:57.140","Text":"That is our final answer."},{"Start":"03:57.140 ","End":"03:59.610","Text":"Thank you very much for watching."}],"ID":23768},{"Watched":false,"Name":"Exercise 6","Duration":"6m 22s","ChapterTopicVideoID":22944,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22944.jpeg","UploadDate":"2020-12-18T04:19:28.4770000","DurationForVideoObject":"PT6M22S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.864","Text":"Hi. We\u0027re going to solve the following exercise."},{"Start":"00:02.864 ","End":"00:08.130","Text":"Calculate the energy in joule corresponding to n equals 7 in a hydrogen atom."},{"Start":"00:08.130 ","End":"00:11.310","Text":"We want to find the energy of the 7th level,"},{"Start":"00:11.310 ","End":"00:16.605","Text":"so the energy of a certain level equals minus RH,"},{"Start":"00:16.605 ","End":"00:19.935","Text":"which is the Rydberg constant,"},{"Start":"00:19.935 ","End":"00:25.710","Text":"divided by n squared and n is the level of the energy."},{"Start":"00:25.710 ","End":"00:28.455","Text":"In our case, we have n equal 7."},{"Start":"00:28.455 ","End":"00:31.170","Text":"We\u0027re just going to E7,"},{"Start":"00:31.170 ","End":"00:34.154","Text":"which is the energy of the 7th that will equals minus,"},{"Start":"00:34.154 ","End":"00:39.420","Text":"RH is just to 0.179 times 10 to"},{"Start":"00:39.420 ","End":"00:46.025","Text":"the negative 18 joule and all of this is divided by n squared."},{"Start":"00:46.025 ","End":"00:47.850","Text":"And again, n equals 7,"},{"Start":"00:47.850 ","End":"00:52.680","Text":"so divided by 7 squared and this gives us minus"},{"Start":"00:52.680 ","End":"00:58.930","Text":"4.45 times 10 to the negative 20 joule."},{"Start":"00:58.930 ","End":"01:04.715","Text":"Final answer is minus 4.45 times 10 to the negative 20 joule."},{"Start":"01:04.715 ","End":"01:07.680","Text":"Thank you very much for watching."}],"ID":23769},{"Watched":false,"Name":"Exercise 7","Duration":"2m 8s","ChapterTopicVideoID":22937,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22937.jpeg","UploadDate":"2020-12-18T04:17:17.1070000","DurationForVideoObject":"PT2M8S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.865","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:02.865 ","End":"00:05.475","Text":"A, calculate the energy loss Delta e,"},{"Start":"00:05.475 ","End":"00:11.655","Text":"when an electron and a hydrogen atom undergoes a transition from n=4 to n=2."},{"Start":"00:11.655 ","End":"00:14.895","Text":"B, calculate the frequency of the emitted photon."},{"Start":"00:14.895 ","End":"00:17.160","Text":"In a, we have to calculate the energy"},{"Start":"00:17.160 ","End":"00:21.015","Text":"lost when an electron undergoes a certain transition."},{"Start":"00:21.015 ","End":"00:29.100","Text":"We\u0027re going to use the equation Delta e. The difference in the energy equals minus RH,"},{"Start":"00:29.100 ","End":"00:31.740","Text":"RH is the Rydberg constant,"},{"Start":"00:31.740 ","End":"00:39.060","Text":"times 1 divided by the final level squared minus 1 divided by the initial level squared."},{"Start":"00:39.950 ","End":"00:43.560","Text":"In our case, Delta e equals,"},{"Start":"00:43.560 ","End":"00:46.050","Text":"again, minus the Rydberg constant,"},{"Start":"00:46.050 ","End":"00:51.150","Text":"so it\u0027s minus 2.179 times 10^negative"},{"Start":"00:51.150 ","End":"00:59.000","Text":"18 joules times 1 divided by the final level squared,"},{"Start":"00:59.000 ","End":"01:01.760","Text":"and the final level is n=2,"},{"Start":"01:01.760 ","End":"01:07.310","Text":"so 1 divided by 2 squared minus 1 divided by the initial level squared,"},{"Start":"01:07.310 ","End":"01:11.145","Text":"meaning 1 divided by 4 squared."},{"Start":"01:11.145 ","End":"01:21.210","Text":"This equals minus 4.09 times 10^negative 19 joule."},{"Start":"01:21.210 ","End":"01:22.860","Text":"That\u0027s our answer for a,"},{"Start":"01:22.860 ","End":"01:25.520","Text":"that\u0027s the Delta energy that we found."},{"Start":"01:25.520 ","End":"01:30.965","Text":"Now I just want to comment that this energy is negative since the energy here is lost."},{"Start":"01:30.965 ","End":"01:32.570","Text":"The energy is emitted."},{"Start":"01:32.570 ","End":"01:36.365","Text":"Now in b, we have to calculate the frequency of the emitted photon."},{"Start":"01:36.365 ","End":"01:43.510","Text":"First of all, the energy of the photon equals the Delta e,"},{"Start":"01:43.760 ","End":"01:47.240","Text":"the difference in the energy which is emitted."},{"Start":"01:47.240 ","End":"01:51.530","Text":"However, we take the positive value"},{"Start":"01:51.530 ","End":"01:55.775","Text":"of this energy since now we\u0027re talking about the photon."},{"Start":"01:55.775 ","End":"02:00.955","Text":"The energy of the photon also equals h Nu."},{"Start":"02:00.955 ","End":"02:05.400","Text":"H is Planck\u0027s constant and Nu is the frequency."},{"Start":"02:05.400 ","End":"02:10.400","Text":"We\u0027re looking for the frequency therefore we\u0027re going to use Nu equals"},{"Start":"02:10.400 ","End":"02:16.730","Text":"the energy of the photon divided by Planck\u0027s constant."},{"Start":"02:16.730 ","End":"02:20.045","Text":"Again, the energy of the photon is what we found in a,"},{"Start":"02:20.045 ","End":"02:22.400","Text":"however, it\u0027s the positive value of what we found in a,"},{"Start":"02:22.400 ","End":"02:28.250","Text":"so it\u0027s 4.09 times 10^negative 19 joule."},{"Start":"02:28.250 ","End":"02:31.595","Text":"I\u0027m going to divide this by Planck\u0027s constant which is"},{"Start":"02:31.595 ","End":"02:40.605","Text":"6.626 times 10^negative 34 joule times second."},{"Start":"02:40.605 ","End":"02:44.790","Text":"The joules will cancel out and this equals"},{"Start":"02:44.790 ","End":"02:52.650","Text":"6.17 times 10^14 inverse second."},{"Start":"02:52.650 ","End":"02:57.765","Text":"Since it\u0027s 1 divided by s it\u0027s the same as s minus 1 inverse second."},{"Start":"02:57.765 ","End":"03:01.090","Text":"The frequency that we found for the emitted photon,"},{"Start":"03:01.090 ","End":"03:07.890","Text":"Nu equals 6.17 times 10^14 inverse second."},{"Start":"03:07.890 ","End":"03:10.145","Text":"That is your final answer for b."},{"Start":"03:10.145 ","End":"03:12.720","Text":"Thank you very much for listening."}],"ID":23762},{"Watched":false,"Name":"Exercise 8","Duration":"6m 58s","ChapterTopicVideoID":22938,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22938.jpeg","UploadDate":"2020-12-18T04:17:48.5270000","DurationForVideoObject":"PT6M58S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.685","Text":"Hi. We\u0027re going to solve the following exercise."},{"Start":"00:02.685 ","End":"00:04.280","Text":"Calculate the frequency in Hertz,"},{"Start":"00:04.280 ","End":"00:07.650","Text":"and wavelength in nanometers of a photon emitted as a result of"},{"Start":"00:07.650 ","End":"00:12.345","Text":"an electron transition from n equals 7 to n equals 3 in a hydrogen atom."},{"Start":"00:12.345 ","End":"00:16.223","Text":"We have a transition again from n equals 7 to n equals 3,"},{"Start":"00:16.223 ","End":"00:19.770","Text":"and we want to calculate the frequency and the wavelength of the photon emitted."},{"Start":"00:19.770 ","End":"00:25.965","Text":"Now we know that the energy of the photon equals h Nu,"},{"Start":"00:25.965 ","End":"00:32.040","Text":"and we also know that the difference in energy between the levels equals minus R_H,"},{"Start":"00:32.040 ","End":"00:34.470","Text":"which is the Rydberg\u0027s constant times 1 divided by"},{"Start":"00:34.470 ","End":"00:39.015","Text":"the final level squared minus 1 divided by the initial level squared."},{"Start":"00:39.015 ","End":"00:42.570","Text":"Now since we\u0027re interested in the photon\u0027s energy,"},{"Start":"00:42.570 ","End":"00:47.210","Text":"the energy of the photon is the positive value of"},{"Start":"00:47.210 ","End":"00:51.770","Text":"Delta E. Now we\u0027re"},{"Start":"00:51.770 ","End":"00:53.330","Text":"going to look at the frequency because we want"},{"Start":"00:53.330 ","End":"00:56.435","Text":"to calculate the frequency of the emitted photon."},{"Start":"00:56.435 ","End":"01:01.550","Text":"The frequency, just going to divide both sides by Planck\u0027s constant,"},{"Start":"01:01.550 ","End":"01:07.310","Text":"equals the energy of the photon divided by Planck\u0027s constant,"},{"Start":"01:07.310 ","End":"01:13.250","Text":"which is h. The energy of the photon also equals the positive value of Delta E,"},{"Start":"01:13.250 ","End":"01:16.505","Text":"meaning equals R_H,"},{"Start":"01:16.505 ","End":"01:18.155","Text":"the Rydberg\u0027s constant,"},{"Start":"01:18.155 ","End":"01:21.635","Text":"times 1 divided by the final level squared,"},{"Start":"01:21.635 ","End":"01:25.510","Text":"minus 1 divided by the initial level squared."},{"Start":"01:25.510 ","End":"01:27.440","Text":"All of this, as you can see,"},{"Start":"01:27.440 ","End":"01:30.990","Text":"is we have to divide by Planck\u0027s constant so Nu,"},{"Start":"01:30.990 ","End":"01:33.675","Text":"the frequency equals R_H,"},{"Start":"01:33.675 ","End":"01:34.860","Text":"which is the Rydberg\u0027s constant,"},{"Start":"01:34.860 ","End":"01:38.080","Text":"divided by h which is Planck\u0027s constant times 1"},{"Start":"01:38.080 ","End":"01:42.200","Text":"divided by the final level squared minus 1 divided by the initial level squared."},{"Start":"01:42.200 ","End":"01:51.424","Text":"This equals the Rydberg\u0027s constant is 2.179 times 10 to the negative 18 joule"},{"Start":"01:51.424 ","End":"01:54.500","Text":"divided by Planck\u0027s constant which is"},{"Start":"01:54.500 ","End":"02:01.595","Text":"6.66 times 10 to the negative 34 joules times seconds."},{"Start":"02:01.595 ","End":"02:03.170","Text":"Joules cancel out,"},{"Start":"02:03.170 ","End":"02:06.650","Text":"and all of this is times 1 divided by the final level,"},{"Start":"02:06.650 ","End":"02:08.030","Text":"which is 3,"},{"Start":"02:08.030 ","End":"02:10.995","Text":"so 3^2 minus,"},{"Start":"02:10.995 ","End":"02:15.360","Text":"1 divided by the initial level squared which is 7, so 7^2."},{"Start":"02:15.360 ","End":"02:24.995","Text":"This equals 2.98 times 10^14 and we\u0027re left with inverse second."},{"Start":"02:24.995 ","End":"02:29.070","Text":"That is the frequency of the emitted photon."},{"Start":"02:29.260 ","End":"02:32.150","Text":"That\u0027s the frequency of the emitted photon in"},{"Start":"02:32.150 ","End":"02:35.150","Text":"inverse seconds land inverse seconds also equals Hertz,"},{"Start":"02:35.150 ","End":"02:40.920","Text":"so this also equals 2.98 times 10^14 hertz."},{"Start":"02:43.700 ","End":"02:47.780","Text":"Now we\u0027re asked to find the wavelength of this emitted photon."},{"Start":"02:47.780 ","End":"02:52.550","Text":"For this purpose, we\u0027re going to use the equation c equals Lambda Nu."},{"Start":"02:52.550 ","End":"02:55.565","Text":"C is the speed of light constant,"},{"Start":"02:55.565 ","End":"02:57.050","Text":"Lambda is the wavelength,"},{"Start":"02:57.050 ","End":"02:58.355","Text":"and Nu is the frequency."},{"Start":"02:58.355 ","End":"03:00.665","Text":"Now we know Nu, and we have to find Lambda."},{"Start":"03:00.665 ","End":"03:04.280","Text":"We\u0027re going to divide both sides by Nu, by the frequency,"},{"Start":"03:04.280 ","End":"03:10.540","Text":"and that\u0027s going to give us Lambda equals c divided by Nu."},{"Start":"03:10.910 ","End":"03:15.110","Text":"C again is the speed of light constant that equals 3 times 10^8"},{"Start":"03:15.110 ","End":"03:21.640","Text":"meters per second divided by Nu which is the frequency,"},{"Start":"03:21.640 ","End":"03:23.820","Text":"which we found in A,"},{"Start":"03:23.820 ","End":"03:32.445","Text":"which equals 2.98 times 10^14 inverse seconds."},{"Start":"03:32.445 ","End":"03:40.330","Text":"After dividing, we get 1.01 times 10 to the negative 6 meters."},{"Start":"03:40.330 ","End":"03:42.875","Text":"I want you to take quick look at the units."},{"Start":"03:42.875 ","End":"03:49.250","Text":"We have meters per second divided by inverse second,"},{"Start":"03:49.250 ","End":"03:53.000","Text":"which is 1 divided by s. When you have a fraction divided by the fraction,"},{"Start":"03:53.000 ","End":"03:56.330","Text":"you multiply the numerator and the denominator,"},{"Start":"03:56.330 ","End":"03:58.400","Text":"and you multiply it again,"},{"Start":"03:58.400 ","End":"03:59.990","Text":"the numerator and the denominator."},{"Start":"03:59.990 ","End":"04:01.355","Text":"This equals, if we look,"},{"Start":"04:01.355 ","End":"04:07.260","Text":"meters times second divided by second times 1 which is seconds,"},{"Start":"04:07.260 ","End":"04:08.480","Text":"so the seconds cancel out,"},{"Start":"04:08.480 ","End":"04:10.695","Text":"and we\u0027re left with meters."},{"Start":"04:10.695 ","End":"04:13.785","Text":"Our units are meters."},{"Start":"04:13.785 ","End":"04:16.560","Text":"This 10 to the minus 6 is micro,"},{"Start":"04:16.560 ","End":"04:20.200","Text":"so it equals 1.1 micrometer."},{"Start":"04:20.200 ","End":"04:24.365","Text":"The wavelength that we found equals 1.01 micrometer,"},{"Start":"04:24.365 ","End":"04:26.660","Text":"the wavelength of the emitted photon."},{"Start":"04:26.660 ","End":"04:28.220","Text":"That is our final answer."},{"Start":"04:28.220 ","End":"04:30.750","Text":"Thank you very much for watching."}],"ID":23763},{"Watched":false,"Name":"Radial Wavefunctions","Duration":"7m 30s","ChapterTopicVideoID":20165,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20165.jpeg","UploadDate":"2019-07-10T23:33:50.6030000","DurationForVideoObject":"PT7M30S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.740","Text":"In the previous videos,"},{"Start":"00:01.740 ","End":"00:05.880","Text":"we talked about the wavefunctions and energy levels of the hydrogen atom."},{"Start":"00:05.880 ","End":"00:09.705","Text":"In this video, we\u0027ll describe the radial part of the wavefunction."},{"Start":"00:09.705 ","End":"00:12.930","Text":"Let\u0027s recall that a wave function has a radial part,"},{"Start":"00:12.930 ","End":"00:14.400","Text":"and an angular part."},{"Start":"00:14.400 ","End":"00:17.835","Text":"This video we\u0027re going to concentrate on the radial part."},{"Start":"00:17.835 ","End":"00:20.910","Text":"Here\u0027s the wavefunction, written mathematically."},{"Start":"00:20.910 ","End":"00:24.090","Text":"Psi is equal to product of capital R,"},{"Start":"00:24.090 ","End":"00:26.590","Text":"which is the radial part,"},{"Start":"00:26.900 ","End":"00:31.185","Text":"and capital Y, which is the angular part."},{"Start":"00:31.185 ","End":"00:35.490","Text":"Now the radial part only depends on 2 quantum numbers,"},{"Start":"00:35.490 ","End":"00:40.690","Text":"n and l. It\u0027s different for every subshell."},{"Start":"00:40.750 ","End":"00:43.250","Text":"Whereas the angular part,"},{"Start":"00:43.250 ","End":"00:51.570","Text":"only depends on l and ml as independent of n. It\u0027s the same for every shell."},{"Start":"00:56.740 ","End":"01:01.190","Text":"We\u0027re going to begin by talking about the s orbitals."},{"Start":"01:01.190 ","End":"01:07.160","Text":"Here, the mathematical expressions for the radial wave functions for 1s, 2s, and 3s."},{"Start":"01:07.160 ","End":"01:11.600","Text":"I\u0027ve written this in terms of the variable Sigma,"},{"Start":"01:11.600 ","End":"01:16.240","Text":"which is equal to 2Z times r divided by na_0."},{"Start":"01:16.240 ","End":"01:23.160","Text":"Sigma is proportional to r. Sigma changes as n changes."},{"Start":"01:23.160 ","End":"01:27.440","Text":"As n increases, sigma decreases."},{"Start":"01:27.440 ","End":"01:32.705","Text":"The exponential decay in each case is different."},{"Start":"01:32.705 ","End":"01:35.530","Text":"Now we\u0027re going to plot R_nl,"},{"Start":"01:35.530 ","End":"01:38.900","Text":"and we\u0027re going to divide it by this constant Z"},{"Start":"01:38.900 ","End":"01:42.970","Text":"over a0 to the power 3/2, which appears everywhere."},{"Start":"01:42.970 ","End":"01:45.045","Text":"Just to make life simpler."},{"Start":"01:45.045 ","End":"01:48.770","Text":"Then we\u0027re also going to plot the square of this."},{"Start":"01:48.770 ","End":"01:51.845","Text":"We\u0027re going to assume that Z= 1."},{"Start":"01:51.845 ","End":"01:53.330","Text":"Here are our graphs,"},{"Start":"01:53.330 ","End":"01:54.770","Text":"on the left-hand side,"},{"Start":"01:54.770 ","End":"01:56.615","Text":"we have R_nl,"},{"Start":"01:56.615 ","End":"02:00.670","Text":"and the right-hand side, R_nl^2."},{"Start":"02:00.670 ","End":"02:04.890","Text":"We\u0027re plotting as a function of R_ao."},{"Start":"02:04.890 ","End":"02:06.930","Text":"The blue is a 1s,"},{"Start":"02:06.930 ","End":"02:08.940","Text":"the red is a 2s,"},{"Start":"02:08.940 ","End":"02:13.350","Text":"and the green is a 3s same as the right-hand side,"},{"Start":"02:13.350 ","End":"02:15.090","Text":"blue is 1s,"},{"Start":"02:15.090 ","End":"02:19.120","Text":"red is 2s, and green is 3s."},{"Start":"02:19.120 ","End":"02:23.915","Text":"What can we notice about these graphs?"},{"Start":"02:23.915 ","End":"02:28.955","Text":"The first thing to notice is that the s radial wavefunctions are non-zero,"},{"Start":"02:28.955 ","End":"02:31.895","Text":"are equal to 0 here we see."},{"Start":"02:31.895 ","End":"02:36.155","Text":"There are non-zero and the blue one goes up much higher."},{"Start":"02:36.155 ","End":"02:38.450","Text":"This is somewhat strange."},{"Start":"02:38.450 ","End":"02:41.735","Text":"Why should the electron we saw near the nucleus?"},{"Start":"02:41.735 ","End":"02:43.910","Text":"But in the next video,"},{"Start":"02:43.910 ","End":"02:45.490","Text":"we\u0027ll solve the problem."},{"Start":"02:45.490 ","End":"02:50.240","Text":"The second thing to notice is that as n increases,"},{"Start":"02:50.240 ","End":"02:56.735","Text":"R_nl tends towards 0 at higher values of R. In other words,"},{"Start":"02:56.735 ","End":"02:58.970","Text":"the wavefunctions extent,"},{"Start":"02:58.970 ","End":"03:04.025","Text":"or further R to a higher R as n increases."},{"Start":"03:04.025 ","End":"03:09.135","Text":"Then we can say that 3s is bigger than 2s,"},{"Start":"03:09.135 ","End":"03:10.930","Text":"which is bigger than 1s,"},{"Start":"03:10.930 ","End":"03:15.800","Text":"of course this is all on average because we\u0027re talking about distributions."},{"Start":"03:15.800 ","End":"03:17.975","Text":"The third thing is the number of nodes."},{"Start":"03:17.975 ","End":"03:20.210","Text":"In all the radial wave functions,"},{"Start":"03:20.210 ","End":"03:23.410","Text":"the number of nodes is n minus l minus 1."},{"Start":"03:23.410 ","End":"03:27.780","Text":"Here for s functions l=0."},{"Start":"03:27.780 ","End":"03:30.480","Text":"In this case it\u0027s n minus 1."},{"Start":"03:30.480 ","End":"03:33.059","Text":"If n is 1, we have 0."},{"Start":"03:33.059 ","End":"03:35.685","Text":"If n is 2, we have 1."},{"Start":"03:35.685 ","End":"03:37.680","Text":"If n is 3, we have 2."},{"Start":"03:37.680 ","End":"03:39.850","Text":"That\u0027s the number of nodes."},{"Start":"03:39.850 ","End":"03:44.765","Text":"We can see that quite clearly see 1s decreases exponentially,"},{"Start":"03:44.765 ","End":"03:47.180","Text":"has no nodes, 2s,"},{"Start":"03:47.180 ","End":"03:52.440","Text":"has 1 node, 3s has a node here,"},{"Start":"03:52.440 ","End":"03:54.195","Text":"very close to 2s,"},{"Start":"03:54.195 ","End":"03:57.525","Text":"and yet another 1 here."},{"Start":"03:57.525 ","End":"03:59.265","Text":"Here the number of nodes,"},{"Start":"03:59.265 ","End":"04:01.140","Text":"1s has 0 nodes,"},{"Start":"04:01.140 ","End":"04:04.770","Text":"2s has 1 node and 3s has 2 nodes."},{"Start":"04:04.770 ","End":"04:07.365","Text":"Now let\u0027s talk about P orbitals."},{"Start":"04:07.365 ","End":"04:10.625","Text":"Here are the mathematical expressions for the 2p orbital,"},{"Start":"04:10.625 ","End":"04:12.005","Text":"and the 3p orbital."},{"Start":"04:12.005 ","End":"04:15.830","Text":"Again, we have this Z over a0 to the power 3/2,"},{"Start":"04:15.830 ","End":"04:19.820","Text":"which we\u0027re just going to divide by in order to not include it."},{"Start":"04:19.820 ","End":"04:28.265","Text":"Then we have again exponential decay e to the power minus Sigma over 2 in both cases."},{"Start":"04:28.265 ","End":"04:29.990","Text":"But as we said before,"},{"Start":"04:29.990 ","End":"04:33.500","Text":"the Sigma is different for the 2p and the 3p."},{"Start":"04:33.500 ","End":"04:35.449","Text":"Here are our graphs."},{"Start":"04:35.449 ","End":"04:38.990","Text":"The left-hand side we have R_nl on the right-hand side,"},{"Start":"04:38.990 ","End":"04:49.245","Text":"we have R_nl^2 and the blue is 2p and the red is 3p, 2p and 3p."},{"Start":"04:49.245 ","End":"04:51.919","Text":"Now what can we see from these graphs?"},{"Start":"04:51.919 ","End":"04:57.685","Text":"The first thing to notice is that the p radial wavefunction at 0 R=0,"},{"Start":"04:57.685 ","End":"05:01.430","Text":"unlike the s ones, the beginning is 0."},{"Start":"05:01.430 ","End":"05:05.780","Text":"The second thing to notice is that as n increases,"},{"Start":"05:05.780 ","End":"05:09.032","Text":"R_nl goes to 0 at higher values of R,"},{"Start":"05:09.032 ","End":"05:15.398","Text":"and we said that before we can see the 3p decays much more slowly than 2p,"},{"Start":"05:15.398 ","End":"05:19.240","Text":"so 3p extends further out than 2p."},{"Start":"05:19.240 ","End":"05:21.874","Text":"Again, we can look at the number of nodes."},{"Start":"05:21.874 ","End":"05:25.610","Text":"It again goes as expression n minus l minus 1."},{"Start":"05:25.610 ","End":"05:27.995","Text":"This time l is 1."},{"Start":"05:27.995 ","End":"05:31.315","Text":"We\u0027re talking about n minus 2."},{"Start":"05:31.315 ","End":"05:33.150","Text":"For n =2,"},{"Start":"05:33.150 ","End":"05:34.845","Text":"we have 0 nodes."},{"Start":"05:34.845 ","End":"05:37.230","Text":"For n =3,"},{"Start":"05:37.230 ","End":"05:38.925","Text":"we have 1 node."},{"Start":"05:38.925 ","End":"05:42.130","Text":"Here is 2p with 0 nodes,"},{"Start":"05:42.130 ","End":"05:44.790","Text":"and the 3p with 1 node."},{"Start":"05:44.790 ","End":"05:49.770","Text":"If we were talking about 4p,"},{"Start":"05:49.770 ","End":"05:52.025","Text":"then we would have 2 nodes."},{"Start":"05:52.025 ","End":"05:55.940","Text":"Can see the nodes very clearly from the square."},{"Start":"05:55.940 ","End":"05:57.785","Text":"See here\u0027s a node."},{"Start":"05:57.785 ","End":"06:03.485","Text":"Another thing we should notice that the number of nodes increases as n increases."},{"Start":"06:03.485 ","End":"06:05.135","Text":"At higher energies,"},{"Start":"06:05.135 ","End":"06:06.680","Text":"there are more nodes,"},{"Start":"06:06.680 ","End":"06:09.665","Text":"and that\u0027s quite common in quantum mechanics."},{"Start":"06:09.665 ","End":"06:12.488","Text":"Now we\u0027re going to compare 3s,"},{"Start":"06:12.488 ","End":"06:14.345","Text":"3p, and 3d orbitals."},{"Start":"06:14.345 ","End":"06:16.690","Text":"Here\u0027s expression for 3d,"},{"Start":"06:16.690 ","End":"06:20.135","Text":"again, it decays exponentially."},{"Start":"06:20.135 ","End":"06:24.245","Text":"We\u0027ve already had the expressions for 3s and 3p."},{"Start":"06:24.245 ","End":"06:26.570","Text":"Let\u0027s draw them. Again,"},{"Start":"06:26.570 ","End":"06:30.630","Text":"we\u0027re drawing R_nl as a function of R over a0."},{"Start":"06:30.630 ","End":"06:34.365","Text":"The blue is 3s,"},{"Start":"06:34.365 ","End":"06:40.810","Text":"the red is 3p and the green is 3d."},{"Start":"06:40.810 ","End":"06:43.160","Text":"Again, we can look at the number of nodes,"},{"Start":"06:43.160 ","End":"06:45.515","Text":"3s has 2 nodes,"},{"Start":"06:45.515 ","End":"06:49.140","Text":"here is 1 and another one,"},{"Start":"06:49.140 ","End":"06:51.405","Text":"3p has 1 node,"},{"Start":"06:51.405 ","End":"06:57.210","Text":"3p the red 1 we can see it has a node here and 3d has no nodes,"},{"Start":"06:57.210 ","End":"06:58.820","Text":"3d is the green one,"},{"Start":"06:58.820 ","End":"07:02.560","Text":"just rises and decays exponentially."},{"Start":"07:02.560 ","End":"07:08.470","Text":"Another thing we can notice if we compare 3d and 3p,"},{"Start":"07:08.470 ","End":"07:11.380","Text":"comparing the green with the red,"},{"Start":"07:11.380 ","End":"07:19.036","Text":"we see that the main peak of the 3d is at a larger value of R than the main peak of 3p,"},{"Start":"07:19.036 ","End":"07:24.425","Text":"so 3d extends further than 3p."},{"Start":"07:24.425 ","End":"07:30.080","Text":"In this video, we discussed the radial part of the wavefunctions."}],"ID":20940},{"Watched":false,"Name":"Radial Distribution Function","Duration":"3m 44s","ChapterTopicVideoID":20166,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20166.jpeg","UploadDate":"2019-07-10T23:34:26.8270000","DurationForVideoObject":"PT3M44S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.740","Text":"In a previous video,"},{"Start":"00:01.740 ","End":"00:05.490","Text":"we discussed the radial wave function for the hydrogen atom."},{"Start":"00:05.490 ","End":"00:07.890","Text":"Let\u0027s recall what we learned about"},{"Start":"00:07.890 ","End":"00:12.570","Text":"the radial wave functions and probability density for the s orbitals."},{"Start":"00:12.570 ","End":"00:16.763","Text":"What we saw was that the radio wave functions and probability density of"},{"Start":"00:16.763 ","End":"00:21.435","Text":"the s orbitals are non-zero at r equal=0,"},{"Start":"00:21.435 ","End":"00:27.330","Text":"that means that the electron has a non-zero probability to be found at the nucleus."},{"Start":"00:27.330 ","End":"00:29.580","Text":"This is somewhat strange,"},{"Start":"00:29.580 ","End":"00:31.880","Text":"we expect that the electron were"},{"Start":"00:31.880 ","End":"00:36.995","Text":"a certain distance from the nucleus and not sitting on top of it."},{"Start":"00:36.995 ","End":"00:43.715","Text":"The problem can be corrected by learning about the radial distribution function."},{"Start":"00:43.715 ","End":"00:47.900","Text":"Now what we learned before about the radio wave function is correct,"},{"Start":"00:47.900 ","End":"00:51.410","Text":"but it\u0027s correct for any particular direction."},{"Start":"00:51.410 ","End":"00:53.270","Text":"If we want a true picture,"},{"Start":"00:53.270 ","End":"00:57.290","Text":"we need to sum the probability over all possible directions."},{"Start":"00:57.290 ","End":"01:01.430","Text":"For example, the 1s orbital is like a sphere,"},{"Start":"01:01.430 ","End":"01:03.395","Text":"we\u0027ll see that in the next video."},{"Start":"01:03.395 ","End":"01:07.475","Text":"What we calculated was in a particular direction."},{"Start":"01:07.475 ","End":"01:13.700","Text":"Now we need to sum the probability over all the directions."},{"Start":"01:13.700 ","End":"01:17.540","Text":"When we do that, we get the radial distribution function,"},{"Start":"01:17.540 ","End":"01:24.540","Text":"P_nl over r = r^2 Rnl^2."},{"Start":"01:24.770 ","End":"01:29.840","Text":"We need to take the radial wave function and square it,"},{"Start":"01:29.840 ","End":"01:32.930","Text":"and then multiply by r^2,"},{"Start":"01:32.930 ","End":"01:37.490","Text":"it\u0027s a function of r because it changes as r changes."},{"Start":"01:37.490 ","End":"01:44.790","Text":"Now this is much better because now we see that when r=0, p=0."},{"Start":"01:44.950 ","End":"01:51.520","Text":"There is a 0 chance of finding the electron on the nucleus."},{"Start":"01:51.520 ","End":"01:54.405","Text":"Here\u0027s a graph which illustrates this,"},{"Start":"01:54.405 ","End":"02:00.530","Text":"here\u0027s P1s is a function of r over a0 for the 1s orbital,"},{"Start":"02:00.530 ","End":"02:03.050","Text":"we see that begins at 0,"},{"Start":"02:03.050 ","End":"02:07.610","Text":"goes up to maximum and then decreases exponentially."},{"Start":"02:07.610 ","End":"02:09.950","Text":"Now, where is this maximum?"},{"Start":"02:09.950 ","End":"02:13.115","Text":"The maximum is here, 1."},{"Start":"02:13.115 ","End":"02:17.780","Text":"The maximum is when r over a0=1,"},{"Start":"02:17.780 ","End":"02:20.155","Text":"then r = a_0."},{"Start":"02:20.155 ","End":"02:24.165","Text":"We get the maximum at the Bohr radius,"},{"Start":"02:24.165 ","End":"02:29.470","Text":"that\u0027s a very nice result because according to Bohr,"},{"Start":"02:29.470 ","End":"02:37.010","Text":"the electron can be at various distances from the nucleus and the lowest orbital,"},{"Start":"02:37.010 ","End":"02:40.490","Text":"the orbital nearest the nucleus,"},{"Start":"02:40.490 ","End":"02:46.820","Text":"r1 = 1^2 times a_0,"},{"Start":"02:46.820 ","End":"02:52.655","Text":"r1 =a_0, precisely the same,"},{"Start":"02:52.655 ","End":"02:57.076","Text":"except that the according to Bohr,"},{"Start":"02:57.076 ","End":"03:01.670","Text":"the radius is precisely is 0."},{"Start":"03:01.670 ","End":"03:05.900","Text":"Electron is precisely moving on this orbit."},{"Start":"03:05.900 ","End":"03:08.674","Text":"He called it an orbit rather than orbital."},{"Start":"03:08.674 ","End":"03:11.540","Text":"Whereas in our picture,"},{"Start":"03:11.540 ","End":"03:16.640","Text":"there is a probability and the highest probability is at a_0."},{"Start":"03:16.640 ","End":"03:21.005","Text":"But there\u0027s also a non-zero probability for all different values of"},{"Start":"03:21.005 ","End":"03:27.620","Text":"r. That\u0027s the difference between the Bohr model and Schrodinger."},{"Start":"03:27.620 ","End":"03:32.225","Text":"Schrodinger tells us that there is a probability distribution,"},{"Start":"03:32.225 ","End":"03:35.090","Text":"not a particular radius."},{"Start":"03:35.090 ","End":"03:40.010","Text":"This video, we talked about radial distribution functions,"},{"Start":"03:40.010 ","End":"03:44.760","Text":"especially those for the s orbitals."}],"ID":20941},{"Watched":false,"Name":"Angular Wavefunctions","Duration":"6m 1s","ChapterTopicVideoID":20167,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20167.jpeg","UploadDate":"2019-11-07T00:57:21.1070000","DurationForVideoObject":"PT6M1S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.770","Text":"In a previous video,"},{"Start":"00:01.770 ","End":"00:04.890","Text":"we talked about the radial part of the wave function."},{"Start":"00:04.890 ","End":"00:08.520","Text":"In this video, we\u0027ll discuss the angular part."},{"Start":"00:08.520 ","End":"00:13.710","Text":"Let\u0027s recall that the wave function has a radial and an angular part."},{"Start":"00:13.710 ","End":"00:16.340","Text":"Mathematically, we write that as psi,"},{"Start":"00:16.340 ","End":"00:17.720","Text":"which is the wave function."},{"Start":"00:17.720 ","End":"00:20.300","Text":"Is equal to r radial part,"},{"Start":"00:20.300 ","End":"00:22.430","Text":"times y, the angular part."},{"Start":"00:22.430 ","End":"00:31.000","Text":"The angular part has dependence only on 2 quantum numbers, l and ml."},{"Start":"00:31.000 ","End":"00:33.810","Text":"Let\u0027s first talk about the s orbital,"},{"Start":"00:33.810 ","End":"00:36.300","Text":"the angular part, Y_00."},{"Start":"00:36.300 ","End":"00:43.235","Text":"It\u0027s called Y_00 because l=0 and ml=0."},{"Start":"00:43.235 ","End":"00:46.400","Text":"We\u0027re going to write that for short as Y for"},{"Start":"00:46.400 ","End":"00:51.530","Text":"the s orbital and that\u0027s equal to the square root of 1 over 4Pi."},{"Start":"00:51.530 ","End":"00:54.560","Text":"There\u0027s no actual angular dependence."},{"Start":"00:54.560 ","End":"00:57.685","Text":"We don\u0027t see Theta or Phi written here."},{"Start":"00:57.685 ","End":"01:01.560","Text":"For that reason, the s orbital is the same in all directions,"},{"Start":"01:01.560 ","End":"01:03.214","Text":"so it looks like a sphere,"},{"Start":"01:03.214 ","End":"01:05.870","Text":"and its cross-section, like a circle."},{"Start":"01:05.870 ","End":"01:09.380","Text":"There is no node, that means there\u0027s no place where it\u0027s 0,"},{"Start":"01:09.380 ","End":"01:12.290","Text":"and so it always has the same sign."},{"Start":"01:12.290 ","End":"01:17.510","Text":"Here\u0027s a picture, here\u0027s the cross-section in the x, z plane."},{"Start":"01:17.510 ","End":"01:21.455","Text":"It looks like a circle and we\u0027ve written the sign positive"},{"Start":"01:21.455 ","End":"01:26.090","Text":"because there is no change of sign. There\u0027s no node."},{"Start":"01:26.090 ","End":"01:32.120","Text":"Sometimes you\u0027ll see the positive written within the circle."},{"Start":"01:32.120 ","End":"01:35.495","Text":"Now, let\u0027s talk about the p orbitals."},{"Start":"01:35.495 ","End":"01:40.260","Text":"Remember that there are 3 p orbitals;"},{"Start":"01:43.180 ","End":"01:48.010","Text":"there\u0027s P_z, P_x, and P_y."},{"Start":"01:48.010 ","End":"01:53.975","Text":"It\u0027s only P_z that can be clearly written in terms of l and ml."},{"Start":"01:53.975 ","End":"01:58.655","Text":"For P_z, l=1, ml=0,"},{"Start":"01:58.655 ","End":"02:00.640","Text":"the others are combinations."},{"Start":"02:00.640 ","End":"02:03.125","Text":"In this case, it doesn\u0027t really matter."},{"Start":"02:03.125 ","End":"02:06.050","Text":"What we have is an expression for P_z,"},{"Start":"02:06.050 ","End":"02:08.180","Text":"an expression for P_x,"},{"Start":"02:08.180 ","End":"02:09.725","Text":"an expression for P_y."},{"Start":"02:09.725 ","End":"02:12.935","Text":"Now, the expression for P_z is a,"},{"Start":"02:12.935 ","End":"02:14.780","Text":"which is constant,"},{"Start":"02:14.780 ","End":"02:20.160","Text":"a is equal to the square root of 3 over 4Pi times cosine Theta,"},{"Start":"02:20.160 ","End":"02:22.410","Text":"so we have a cosine Theta."},{"Start":"02:22.410 ","End":"02:27.260","Text":"For P_x we have a sine Theta cosine Phi,"},{"Start":"02:27.260 ","End":"02:32.680","Text":"and for P_y, we have a sine Theta sine Phi."},{"Start":"02:32.680 ","End":"02:37.445","Text":"Now, if you recall what we learned about the spherical polar coordinates,"},{"Start":"02:37.445 ","End":"02:44.680","Text":"you\u0027ll recognize that cosine Theta is just z over r. In the case of P_x,"},{"Start":"02:44.680 ","End":"02:50.010","Text":"sine Theta cosine Phi is just x over r. For P_y,"},{"Start":"02:50.010 ","End":"02:57.225","Text":"sine Theta sine Phi is just y over r. P_z is proportion to z,"},{"Start":"02:57.225 ","End":"03:00.285","Text":"and P_x is proportional to x,"},{"Start":"03:00.285 ","End":"03:03.165","Text":"and P_y is proportional to y."},{"Start":"03:03.165 ","End":"03:08.360","Text":"From all that we can conclude that the 3 p orbitals point in x,"},{"Start":"03:08.360 ","End":"03:10.490","Text":"y, and z directions."},{"Start":"03:10.490 ","End":"03:14.905","Text":"They\u0027re identical, they just point in different directions."},{"Start":"03:14.905 ","End":"03:19.700","Text":"What we\u0027re going to do is to draw the angular part of the P_z orbital,"},{"Start":"03:19.700 ","End":"03:21.635","Text":"which is the simplest one."},{"Start":"03:21.635 ","End":"03:25.550","Text":"Now the distance from the origin to a point on the curve"},{"Start":"03:25.550 ","End":"03:31.230","Text":"gives us the absolute value of the angular part for P_z."},{"Start":"03:31.240 ","End":"03:36.550","Text":"It\u0027s this distance, all this distance."},{"Start":"03:36.550 ","End":"03:40.070","Text":"That\u0027s proportional to the absolute value of cosine Theta."},{"Start":"03:40.070 ","End":"03:44.645","Text":"What we\u0027ve drawn here is the absolute value of cosine Theta."},{"Start":"03:44.645 ","End":"03:47.735","Text":"Let\u0027s see, some points on this graph."},{"Start":"03:47.735 ","End":"03:54.740","Text":"This Theta=0, cosine Theta=1,"},{"Start":"03:54.740 ","End":"03:57.110","Text":"so that\u0027s this point here."},{"Start":"03:57.110 ","End":"04:03.570","Text":"If Theta=Pi over 2, cosine Theta=0."},{"Start":"04:05.290 ","End":"04:07.805","Text":"That\u0027s this point here."},{"Start":"04:07.805 ","End":"04:14.070","Text":"If Theta=Pi, cosine Theta=minus 1."},{"Start":"04:14.140 ","End":"04:17.330","Text":"What we\u0027re drawing is the absolute value,"},{"Start":"04:17.330 ","End":"04:19.520","Text":"so what we\u0027re drawing is 1,"},{"Start":"04:19.520 ","End":"04:22.160","Text":"so it\u0027s this point here."},{"Start":"04:22.160 ","End":"04:26.600","Text":"This way we get the right-hand side of this diagram."},{"Start":"04:26.600 ","End":"04:28.790","Text":"In order to get the whole diagram,"},{"Start":"04:28.790 ","End":"04:33.475","Text":"we need to rotate it all by Phi."},{"Start":"04:33.475 ","End":"04:36.225","Text":"Then we get 2 spheres,"},{"Start":"04:36.225 ","End":"04:39.035","Text":"one on the top and one on the bottom."},{"Start":"04:39.035 ","End":"04:44.900","Text":"What\u0027s been drawn here is in fact a cross section in the x, z plane."},{"Start":"04:44.900 ","End":"04:46.805","Text":"We see the 2 spheres."},{"Start":"04:46.805 ","End":"04:49.160","Text":"Now, why are they different colors?"},{"Start":"04:49.160 ","End":"04:52.355","Text":"They\u0027re different colors because there is a node,"},{"Start":"04:52.355 ","End":"04:56.160","Text":"there is a place where there is no probability,"},{"Start":"04:56.160 ","End":"04:59.070","Text":"0 probability of finding the electron,"},{"Start":"04:59.070 ","End":"05:04.925","Text":"so we go from a positive sign to a negative sign through 0."},{"Start":"05:04.925 ","End":"05:06.500","Text":"That\u0027s why we have these signs,"},{"Start":"05:06.500 ","End":"05:10.885","Text":"positive on the top and negative on the bottom."},{"Start":"05:10.885 ","End":"05:13.229","Text":"What we have is 2 circles,"},{"Start":"05:13.229 ","End":"05:17.160","Text":"or 2 spheres pointing along the z-axis,"},{"Start":"05:17.160 ","End":"05:18.695","Text":"and we have a node."},{"Start":"05:18.695 ","End":"05:22.790","Text":"In this one, we have a node and the x-direction because it\u0027s a cross-section."},{"Start":"05:22.790 ","End":"05:26.195","Text":"If we have the total graph, 2 spheres,"},{"Start":"05:26.195 ","End":"05:31.780","Text":"we have a node in the x-y plane."},{"Start":"05:33.460 ","End":"05:37.445","Text":"In order to get the 3-dimensional angular wave function,"},{"Start":"05:37.445 ","End":"05:40.580","Text":"we rotated about the z-axis."},{"Start":"05:40.580 ","End":"05:42.560","Text":"Now, the other orbitals,"},{"Start":"05:42.560 ","End":"05:45.305","Text":"the other p orbitals of the same shape,"},{"Start":"05:45.305 ","End":"05:48.544","Text":"but just point in different directions."},{"Start":"05:48.544 ","End":"05:55.195","Text":"Either the x-direction for P_x or the y-direction for P_y."},{"Start":"05:55.195 ","End":"06:00.900","Text":"In this video, we discussed the angular part of the wave function."}],"ID":20942},{"Watched":false,"Name":"Representations of Orbitals","Duration":"8m 18s","ChapterTopicVideoID":20168,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20168.jpeg","UploadDate":"2019-08-15T02:35:34.5170000","DurationForVideoObject":"PT8M18S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:05.535","Text":"In previous videos, we talked about the radial and angular parts of the wave functions."},{"Start":"00:05.535 ","End":"00:09.990","Text":"In this video, we discuss how to draw the complete wave function."},{"Start":"00:09.990 ","End":"00:13.650","Text":"We\u0027re going to find out how to represent orbitals,"},{"Start":"00:13.650 ","End":"00:17.085","Text":"how to represent orbitals by diagrams."},{"Start":"00:17.085 ","End":"00:22.140","Text":"Now in order to draw the wave function is a function of r, Theta, and Phi."},{"Start":"00:22.140 ","End":"00:24.870","Text":"We would need a 4-dimensional world."},{"Start":"00:24.870 ","End":"00:26.340","Text":"Here\u0027s a wave functions."},{"Start":"00:26.340 ","End":"00:31.050","Text":"First thing, we need to draw 2 dimensions,"},{"Start":"00:31.050 ","End":"00:33.930","Text":"3 dimensions, 4 dimensions."},{"Start":"00:33.930 ","End":"00:36.900","Text":"As you know, we live in a 3-dimensional world."},{"Start":"00:36.900 ","End":"00:42.385","Text":"There are several ways of representing the wave function in our 3-dimensional world."},{"Start":"00:42.385 ","End":"00:45.965","Text":"The first we\u0027re going to talk about is contour maps."},{"Start":"00:45.965 ","End":"00:51.095","Text":"Now I\u0027ll give you 2 examples of the use of contour maps in other places."},{"Start":"00:51.095 ","End":"00:53.705","Text":"For example, in a topographic map,"},{"Start":"00:53.705 ","End":"00:57.635","Text":"there are contours connect places of equal height."},{"Start":"00:57.635 ","End":"01:01.250","Text":"For example, if we want to represent a mountain,"},{"Start":"01:01.250 ","End":"01:04.850","Text":"you can have one contour at a particular height,"},{"Start":"01:04.850 ","End":"01:07.670","Text":"another contour at a higher height,"},{"Start":"01:07.670 ","End":"01:10.835","Text":"and another contour that\u0027s an even higher height."},{"Start":"01:10.835 ","End":"01:14.750","Text":"Now, you may notice that on the right-hand side,"},{"Start":"01:14.750 ","End":"01:19.160","Text":"the lines are closer together than on the left-hand side."},{"Start":"01:19.160 ","End":"01:25.835","Text":"That would indicate that climbing on the right-hand side would be more difficult."},{"Start":"01:25.835 ","End":"01:29.660","Text":"The slope would be steeper than on the left-hand side."},{"Start":"01:29.660 ","End":"01:31.445","Text":"The closer the lines,"},{"Start":"01:31.445 ","End":"01:33.365","Text":"the steeper the hill."},{"Start":"01:33.365 ","End":"01:36.515","Text":"Another example is in weather forecasting."},{"Start":"01:36.515 ","End":"01:39.050","Text":"We have meteorological maps and"},{"Start":"01:39.050 ","End":"01:43.775","Text":"the contours that connect polices of the same barometric pressure."},{"Start":"01:43.775 ","End":"01:48.015","Text":"If we wanted to represent a high H,"},{"Start":"01:48.015 ","End":"01:55.655","Text":"then we would have 1 contour and inner contour at a higher barometric pressure,"},{"Start":"01:55.655 ","End":"01:58.610","Text":"and 1 of even higher barometric pressure."},{"Start":"01:58.610 ","End":"02:00.665","Text":"Of course, if it were a low,"},{"Start":"02:00.665 ","End":"02:07.750","Text":"then we will proceed from higher to lower barometric pressures at the center."},{"Start":"02:07.750 ","End":"02:14.770","Text":"Now for orbitals, we connect points with the same value of absolute value of Psi."},{"Start":"02:14.770 ","End":"02:19.840","Text":"We can do this in either 2-dimensional or 3-dimensional figure."},{"Start":"02:19.840 ","End":"02:21.815","Text":"Here are 2 examples."},{"Start":"02:21.815 ","End":"02:26.435","Text":"Here\u0027s a 1s orbital and 2 px orbital,"},{"Start":"02:26.435 ","End":"02:29.615","Text":"and we\u0027ve drawn them in the x, y plane."},{"Start":"02:29.615 ","End":"02:32.270","Text":"These are 2 dimensional figures."},{"Start":"02:32.270 ","End":"02:39.170","Text":"We see in the 1s orbital that the lines towards the center are getting closer and closer."},{"Start":"02:39.170 ","End":"02:43.990","Text":"That means that the electron density"},{"Start":"02:43.990 ","End":"02:49.745","Text":"of Psi is increasing more rapidly towards the center."},{"Start":"02:49.745 ","End":"02:52.070","Text":"Then the right-hand side,"},{"Start":"02:52.070 ","End":"02:55.270","Text":"the electron density is increasing."},{"Start":"02:55.270 ","End":"02:57.404","Text":"We have 2 lobes."},{"Start":"02:57.404 ","End":"03:01.505","Text":"They are in 2 different colors to indicate 2 signs."},{"Start":"03:01.505 ","End":"03:05.765","Text":"Perhaps this would be positive and this would be negative."},{"Start":"03:05.765 ","End":"03:10.185","Text":"In the center, there\u0027s a nodal plane."},{"Start":"03:10.185 ","End":"03:13.005","Text":"It\u0027s changing from positive to negative."},{"Start":"03:13.005 ","End":"03:17.705","Text":"We see that unlike the angular wave function that we saw before,"},{"Start":"03:17.705 ","End":"03:21.515","Text":"these 2 sides are not just spheres,"},{"Start":"03:21.515 ","End":"03:23.915","Text":"they\u0027re not spheres or circles."},{"Start":"03:23.915 ","End":"03:27.600","Text":"They are distorted ellipsoids."},{"Start":"03:35.510 ","End":"03:41.315","Text":"Now another way of doing this is to draw the electron cloud,"},{"Start":"03:41.315 ","End":"03:46.010","Text":"and after will see from that we can get the boundary surface diagrams."},{"Start":"03:46.010 ","End":"03:48.664","Text":"In an electron cloud diagram,"},{"Start":"03:48.664 ","End":"03:50.840","Text":"the density of shading is"},{"Start":"03:50.840 ","End":"03:54.140","Text":"proportional to the probability of finding the electron at that point,"},{"Start":"03:54.140 ","End":"03:59.200","Text":"probability is proportional to Psi^2, just remember."},{"Start":"03:59.200 ","End":"04:01.460","Text":"The board is a fuzzy,"},{"Start":"04:01.460 ","End":"04:04.250","Text":"since the wave functions decay exponentially,"},{"Start":"04:04.250 ","End":"04:08.935","Text":"we never really can get to a 100 percent probability."},{"Start":"04:08.935 ","End":"04:10.900","Text":"That\u0027s why they are fuzzy."},{"Start":"04:10.900 ","End":"04:16.765","Text":"Here\u0027s a picture of an electron cloud diagram for a 1s orbital,"},{"Start":"04:16.765 ","End":"04:23.380","Text":"we see that the shading is more intense towards the center."},{"Start":"04:23.380 ","End":"04:28.495","Text":"That means the electron density is including towards the center."},{"Start":"04:28.495 ","End":"04:30.730","Text":"Now instead of drawing the cloud,"},{"Start":"04:30.730 ","End":"04:33.550","Text":"one can draw contour within which"},{"Start":"04:33.550 ","End":"04:37.945","Text":"the probability of finding the electron let\u0027s say 90 percent."},{"Start":"04:37.945 ","End":"04:39.910","Text":"Now, what\u0027s the shape of this?"},{"Start":"04:39.910 ","End":"04:43.405","Text":"The shape is similar to what we saw before,"},{"Start":"04:43.405 ","End":"04:46.750","Text":"the distorted ellipsoids that we saw before."},{"Start":"04:46.750 ","End":"04:50.245","Text":"Now if we go back there where we were,"},{"Start":"04:50.245 ","End":"04:54.590","Text":"we\u0027ll see that the shape will look like one of these contours,"},{"Start":"04:54.590 ","End":"04:56.705","Text":"perhaps the outermost contour."},{"Start":"04:56.705 ","End":"04:59.456","Text":"We have a distorted ellipse side on"},{"Start":"04:59.456 ","End":"05:04.445","Text":"the right-hand side and undistorted ellipsoid on the left-hand side."},{"Start":"05:04.445 ","End":"05:07.100","Text":"If we wanted to 3-dimensional picture,"},{"Start":"05:07.100 ","End":"05:13.145","Text":"we would rotate this about the x-axis to get a 3-dimensional picture."},{"Start":"05:13.145 ","End":"05:19.010","Text":"Now this is a very accurate way of depicting a 2px orbital,"},{"Start":"05:19.010 ","End":"05:22.190","Text":"and you\u0027ll see this in many textbooks."},{"Start":"05:22.190 ","End":"05:25.640","Text":"But, it\u0027s not very convenient for everyday use."},{"Start":"05:25.640 ","End":"05:29.825","Text":"Now we\u0027re going to discuss the way that is commonly used,"},{"Start":"05:29.825 ","End":"05:31.580","Text":"perhaps less accurate,"},{"Start":"05:31.580 ","End":"05:33.320","Text":"but easier to use."},{"Start":"05:33.320 ","End":"05:38.615","Text":"We\u0027re going to discuss a simplified representations in common use."},{"Start":"05:38.615 ","End":"05:40.954","Text":"Here\u0027s an S orbital."},{"Start":"05:40.954 ","End":"05:43.145","Text":"It\u0027s drawn in as a sphere."},{"Start":"05:43.145 ","End":"05:45.440","Text":"If we want to just in 2-dimensions,"},{"Start":"05:45.440 ","End":"05:47.660","Text":"we could just draw a circle,"},{"Start":"05:47.660 ","End":"05:52.220","Text":"perhaps with a positive sign inside to indicate that there is no node."},{"Start":"05:52.220 ","End":"05:57.120","Text":"Here are the 3p orbitals drawn in 3-dimensions,"},{"Start":"05:57.120 ","End":"05:59.385","Text":"P_x, P_y, and P_z."},{"Start":"05:59.385 ","End":"06:05.870","Text":"Now, you see 2 different colors to indicate that there is a node."},{"Start":"06:05.870 ","End":"06:09.180","Text":"The orange would be positive z,"},{"Start":"06:09.180 ","End":"06:14.010","Text":"and the green one negative and there is a node in the center."},{"Start":"06:14.010 ","End":"06:18.540","Text":"In this case in the y, z plane."},{"Start":"06:18.540 ","End":"06:21.510","Text":"The same for P_y and P_z."},{"Start":"06:21.510 ","End":"06:27.400","Text":"Now, often even more simple diagrams are used,"},{"Start":"06:27.400 ","End":"06:30.385","Text":"especially when we have to draw them ourselves."},{"Start":"06:30.385 ","End":"06:35.290","Text":"We might just draw P_x like this, positive-negative."},{"Start":"06:35.290 ","End":"06:39.680","Text":"P_y like this positive-negative."},{"Start":"06:39.680 ","End":"06:44.125","Text":"It\u0027s more like a figure of 8, like an 8."},{"Start":"06:44.125 ","End":"06:48.085","Text":"Now up to now we haven\u0027t talked much about d orbitals,"},{"Start":"06:48.085 ","End":"06:52.585","Text":"but here are the simple representations of the d orbitals."},{"Start":"06:52.585 ","End":"06:56.510","Text":"You will recall that there are 5 d orbitals."},{"Start":"06:56.510 ","End":"07:02.750","Text":"Here are 3-dimensional representations of the 5 orbitals."},{"Start":"07:02.750 ","End":"07:04.820","Text":"There\u0027s one in the x,"},{"Start":"07:04.820 ","End":"07:07.520","Text":"y plane on the axis."},{"Start":"07:07.520 ","End":"07:10.685","Text":"That\u0027s called d_(x-y)^2."},{"Start":"07:10.685 ","End":"07:13.200","Text":"There\u0027s one called d_xy,"},{"Start":"07:13.200 ","End":"07:19.280","Text":"where the 4 lobes are in-between the x and y-axis,"},{"Start":"07:19.280 ","End":"07:23.030","Text":"not on the axis like the d_(x-y)^2,"},{"Start":"07:23.030 ","End":"07:28.560","Text":"and there are 3 orbitals similar to d_xy, this d_xy,"},{"Start":"07:28.560 ","End":"07:32.790","Text":"d_xz and d_yz,"},{"Start":"07:32.790 ","End":"07:35.745","Text":"they are all between the axis."},{"Start":"07:35.745 ","End":"07:38.940","Text":"They have 2 nodal planes."},{"Start":"07:38.940 ","End":"07:42.290","Text":"Because we\u0027re going from positive to"},{"Start":"07:42.290 ","End":"07:46.250","Text":"negative and then back to positive and then to negative,"},{"Start":"07:46.250 ","End":"07:49.610","Text":"so there are 2 nodal planes."},{"Start":"07:49.610 ","End":"07:54.910","Text":"The one that looks a bit different is d_z^2."},{"Start":"07:54.910 ","End":"07:58.100","Text":"It also has 2 nodal planes,"},{"Start":"07:58.100 ","End":"07:59.555","Text":"but they\u0027re not planes."},{"Start":"07:59.555 ","End":"08:02.360","Text":"They\u0027re more like conic surfaces."},{"Start":"08:02.360 ","End":"08:05.360","Text":"That\u0027s not particularly important at the moment."},{"Start":"08:05.360 ","End":"08:07.475","Text":"Here we have positive,"},{"Start":"08:07.475 ","End":"08:11.675","Text":"positive and the central part is negative."},{"Start":"08:11.675 ","End":"08:18.810","Text":"In this video, we showed how to represent the various orbitals in several different ways."}],"ID":20943},{"Watched":false,"Name":"Electron Spin","Duration":"5m 47s","ChapterTopicVideoID":20169,"CourseChapterTopicPlaylistID":154570,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20169.jpeg","UploadDate":"2019-11-07T00:59:47.0270000","DurationForVideoObject":"PT5M47S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:04.905","Text":"In previous videos, we learned about the orbitals of the hydrogen atom."},{"Start":"00:04.905 ","End":"00:08.550","Text":"In this video, we\u0027ll talk about the electron spin."},{"Start":"00:08.550 ","End":"00:11.625","Text":"Let\u0027s recall what we learned about orbitals."},{"Start":"00:11.625 ","End":"00:16.320","Text":"A hydrogen like orbital is characterized by 3 quantum numbers,"},{"Start":"00:16.320 ","End":"00:18.870","Text":"n, l, and m_l."},{"Start":"00:18.870 ","End":"00:24.360","Text":"However, these quantum numbers cannot explain all the observed phenomena."},{"Start":"00:24.360 ","End":"00:28.010","Text":"For example, there\u0027s a very small difference in"},{"Start":"00:28.010 ","End":"00:32.780","Text":"frequency between the spectral lines predicted by Bohr and Schrodinger,"},{"Start":"00:32.780 ","End":"00:35.435","Text":"and those observed experimentally."},{"Start":"00:35.435 ","End":"00:41.810","Text":"In addition, the orange emission line of sodium consists of 2 closely spaced lines,"},{"Start":"00:41.810 ","End":"00:44.839","Text":"not 1 is predicted by Schrodinger."},{"Start":"00:44.839 ","End":"00:49.015","Text":"The answer comes from considerations of Spin."},{"Start":"00:49.015 ","End":"00:53.845","Text":"In 1925, Samuel Goudsmit and George Uhlenbeck,"},{"Start":"00:53.845 ","End":"00:59.240","Text":"suggested that the electron has an intrinsic angular momentum in addition to"},{"Start":"00:59.240 ","End":"01:06.465","Text":"the orbital angular momentum given by quantum number l. They called this property Spin."},{"Start":"01:06.465 ","End":"01:13.400","Text":"It\u0027s analogy, is the Earth spinning on its axis while also revolving around the Sun."},{"Start":"01:13.400 ","End":"01:18.169","Text":"The Earth goes around the Sun but in addition,"},{"Start":"01:18.169 ","End":"01:21.675","Text":"it can rotate on its axis."},{"Start":"01:21.675 ","End":"01:25.865","Text":"Now Spin of an electron is much more complicated."},{"Start":"01:25.865 ","End":"01:28.565","Text":"It\u0027s not explained by the Schrodinger equation,"},{"Start":"01:28.565 ","End":"01:30.655","Text":"but by the Dirac equation,"},{"Start":"01:30.655 ","End":"01:32.220","Text":"written by Paul Dirac,"},{"Start":"01:32.220 ","End":"01:36.830","Text":"in 1928, for which he got the Nobel Prize in 1933."},{"Start":"01:36.830 ","End":"01:43.090","Text":"The Dirac equations are combination of Einstein\u0027s relativity and quantum mechanics,"},{"Start":"01:43.090 ","End":"01:45.945","Text":"and it gives us a description of Spin."},{"Start":"01:45.945 ","End":"01:49.900","Text":"Spin is a relativistic effect."},{"Start":"01:56.810 ","End":"02:00.354","Text":"Now let\u0027s talk about the spin of the electron."},{"Start":"02:00.354 ","End":"02:04.720","Text":"Every electron has a spin angular momentum quantum number,"},{"Start":"02:04.720 ","End":"02:07.930","Text":"s is equal to a 1/2."},{"Start":"02:07.930 ","End":"02:10.224","Text":"That\u0027s every single electron."},{"Start":"02:10.224 ","End":"02:11.955","Text":"There\u0027s no variation."},{"Start":"02:11.955 ","End":"02:14.610","Text":"A spin magnetic quantum number m_s."},{"Start":"02:14.610 ","End":"02:18.475","Text":"Now, s is analogous to l,"},{"Start":"02:18.475 ","End":"02:19.930","Text":"we\u0027ve learned about before,"},{"Start":"02:19.930 ","End":"02:24.340","Text":"and m_ s is analogous to ml,"},{"Start":"02:24.340 ","End":"02:27.185","Text":"and m _s can only take 2 values,"},{"Start":"02:27.185 ","End":"02:29.920","Text":"plus a 1/2 or minus a 1/2."},{"Start":"02:29.920 ","End":"02:35.105","Text":"Often we indicate this plus a 1/2 as an arrow pointing upwards,"},{"Start":"02:35.105 ","End":"02:38.600","Text":"and minus a 1/2 as an arrow pointing downwards,"},{"Start":"02:38.600 ","End":"02:40.805","Text":"or sometimes we use Alpha,"},{"Start":"02:40.805 ","End":"02:42.350","Text":"the Greek letter Alpha,"},{"Start":"02:42.350 ","End":"02:44.495","Text":"for m_s equal to plus a 1/2,"},{"Start":"02:44.495 ","End":"02:49.175","Text":"and the Greek letter Beta for m_s equal to minus a 1/2."},{"Start":"02:49.175 ","End":"02:56.435","Text":"The arrow pointing upwards can be related to counter-clockwise spinning of the electron,"},{"Start":"02:56.435 ","End":"03:01.370","Text":"whereas the arrow pointing downwards relates to clockwise spinning."},{"Start":"03:01.370 ","End":"03:05.420","Text":"So the arrow pointing upwards relates to"},{"Start":"03:05.420 ","End":"03:11.630","Text":"spinning anticlockwise or counterclockwise,"},{"Start":"03:11.630 ","End":"03:17.320","Text":"whereas the arrow pointing downwards relates to clockwise spinning."},{"Start":"03:17.320 ","End":"03:22.565","Text":"Both Spin states have the same energy in the absence of a magnetic field."},{"Start":"03:22.565 ","End":"03:24.680","Text":"If there\u0027s a magnetic field,"},{"Start":"03:24.680 ","End":"03:32.135","Text":"there\u0027s a very small difference in energy between the 2 arrows between the 2 spins."},{"Start":"03:32.135 ","End":"03:36.080","Text":"I should mention here that not only does the electron have a spin,"},{"Start":"03:36.080 ","End":"03:40.115","Text":"but many other subatomic particles also have spins."},{"Start":"03:40.115 ","End":"03:47.375","Text":"For example, the spin of the nucleus of the hydrogen atom is equal to a 1/2."},{"Start":"03:47.375 ","End":"03:50.990","Text":"That\u0027s the basis of the phenomena that you\u0027ve perhaps"},{"Start":"03:50.990 ","End":"03:54.380","Text":"heard of, Nuclear Magnetic Resonance,"},{"Start":"03:54.380 ","End":"04:02.310","Text":"NMR, or MRI, Magnetic Resonance Imaging used in medicine."},{"Start":"04:02.310 ","End":"04:05.780","Text":"Let\u0027s describe the ground state of hydrogen."},{"Start":"04:05.780 ","End":"04:07.865","Text":"In order to do it accurately,"},{"Start":"04:07.865 ","End":"04:10.385","Text":"we need 4 quantum numbers;"},{"Start":"04:10.385 ","End":"04:13.860","Text":"n, l, m_l,"},{"Start":"04:13.860 ","End":"04:15.885","Text":"and the new 1, m_s."},{"Start":"04:15.885 ","End":"04:22.165","Text":"We don\u0027t write s itself because it\u0027s always equal to a 1/2 for electron."},{"Start":"04:22.165 ","End":"04:23.660","Text":"For the ground state,"},{"Start":"04:23.660 ","End":"04:27.200","Text":"we have n equal to 1, l equal to 0,"},{"Start":"04:27.200 ","End":"04:29.075","Text":"m_l equal to 0,"},{"Start":"04:29.075 ","End":"04:32.860","Text":"and all that describes the 1s orbital."},{"Start":"04:32.860 ","End":"04:35.989","Text":"An addition, we have the spin of the electron,"},{"Start":"04:35.989 ","End":"04:40.160","Text":"which can either be a 1/2 or minus a 1/2."},{"Start":"04:40.160 ","End":"04:44.555","Text":"We see that the electron occupies the 1s orbital."},{"Start":"04:44.555 ","End":"04:47.150","Text":"It can do so with either spin,"},{"Start":"04:47.150 ","End":"04:50.464","Text":"and we call this a 1s electron."},{"Start":"04:50.464 ","End":"04:54.080","Text":"This 1s electron can have either spin,"},{"Start":"04:54.080 ","End":"04:57.905","Text":"can either have spin up or spin down."},{"Start":"04:57.905 ","End":"04:59.974","Text":"So if we had a 100 electrons,"},{"Start":"04:59.974 ","End":"05:04.675","Text":"50 would be spin up and 50 will spin down."},{"Start":"05:04.675 ","End":"05:08.470","Text":"The number of possible combinations of n, l,"},{"Start":"05:08.470 ","End":"05:13.540","Text":"and m_l, for a particular volume of n is something we calculated before."},{"Start":"05:13.540 ","End":"05:15.565","Text":"We call it the degeneracy,"},{"Start":"05:15.565 ","End":"05:18.730","Text":"because all the orbitals with the same n have"},{"Start":"05:18.730 ","End":"05:22.075","Text":"the same energy when we\u0027re talking about hydrogen,"},{"Start":"05:22.075 ","End":"05:26.735","Text":"and we calculated it to be n^2, we call degeneracy."},{"Start":"05:26.735 ","End":"05:28.880","Text":"If we include also m_s,"},{"Start":"05:28.880 ","End":"05:31.945","Text":"then the number of possible combinations of n,"},{"Start":"05:31.945 ","End":"05:34.165","Text":"l, m_l, and m_s,"},{"Start":"05:34.165 ","End":"05:37.180","Text":"for a particular volume of n is twice as great,"},{"Start":"05:37.180 ","End":"05:43.015","Text":"it\u0027s 2n^2, because we have 2 possible values of m_s."},{"Start":"05:43.015 ","End":"05:47.300","Text":"In this video, we talked about electron spin."}],"ID":20944}],"Thumbnail":null,"ID":154570},{"Name":"Multielectron Atoms","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Multielectron Atoms","Duration":"8m 3s","ChapterTopicVideoID":20173,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20173.jpeg","UploadDate":"2019-08-15T04:29:35.5500000","DurationForVideoObject":"PT8M3S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:04.120","Text":"In previous videos, we talked about the hydrogen atom,"},{"Start":"00:04.120 ","End":"00:06.160","Text":"which only has 1 electron."},{"Start":"00:06.160 ","End":"00:11.770","Text":"In this video, we\u0027ll introduce atoms that have more than 1 electron."},{"Start":"00:11.770 ","End":"00:15.280","Text":"We call such atoms multi-electron,"},{"Start":"00:15.280 ","End":"00:19.930","Text":"or many electron or sometimes poly electron atoms."},{"Start":"00:19.930 ","End":"00:23.840","Text":"In this video, we\u0027ll call them multi-electron atoms."},{"Start":"00:23.840 ","End":"00:30.625","Text":"Now, the Schrodinger equation can only be solved exactly for 2 particles."},{"Start":"00:30.625 ","End":"00:33.535","Text":"As soon as we have more than 2 particles,"},{"Start":"00:33.535 ","End":"00:36.415","Text":"it can only be solved approximately."},{"Start":"00:36.415 ","End":"00:44.195","Text":"Now, one of the approximations used is called self-consistent field theory or SCF."},{"Start":"00:44.195 ","End":"00:47.870","Text":"In this, we assume that each electron moves in"},{"Start":"00:47.870 ","End":"00:52.330","Text":"the field created by the nucleus and all the other electrons,"},{"Start":"00:52.330 ","End":"00:57.380","Text":"involves complicated mathematics and extensive programming."},{"Start":"00:57.380 ","End":"01:01.595","Text":"But the very important thing we need to know is this method gives"},{"Start":"01:01.595 ","End":"01:06.665","Text":"orbitals that have approximately the same shape as the hydrogen orbitals,"},{"Start":"01:06.665 ","End":"01:09.620","Text":"but of course, different energies and different"},{"Start":"01:09.620 ","End":"01:13.670","Text":"radio behavior, different radial dependence."},{"Start":"01:13.670 ","End":"01:16.130","Text":"Now one of the other things is,"},{"Start":"01:16.130 ","End":"01:19.100","Text":"that in a multi-electron atom,"},{"Start":"01:19.100 ","End":"01:24.140","Text":"the orbitals in the same shell are no longer degenerate."},{"Start":"01:24.140 ","End":"01:28.000","Text":"If you remember from the hydrogen atom, 3s,"},{"Start":"01:28.000 ","End":"01:34.595","Text":"3p, and 3d all had the same energies."},{"Start":"01:34.595 ","End":"01:37.580","Text":"However, in multi-electron atoms,"},{"Start":"01:37.580 ","End":"01:42.410","Text":"we find 3s has a lower energy than 3p,"},{"Start":"01:42.410 ","End":"01:45.185","Text":"which has a lower energy than 3d."},{"Start":"01:45.185 ","End":"01:50.315","Text":"Whereas in hydrogen, these orbitals are degenerate."},{"Start":"01:50.315 ","End":"01:54.395","Text":"For example, helium, they are no longer degenerate."},{"Start":"01:54.395 ","End":"02:00.785","Text":"Now, the reason for all this is because when we consider multi-electron atoms,"},{"Start":"02:00.785 ","End":"02:06.010","Text":"we have something else to consider and that\u0027s called electron-electron repulsion."},{"Start":"02:06.010 ","End":"02:09.380","Text":"Let\u0027s take the example of the helium atom."},{"Start":"02:09.380 ","End":"02:16.085","Text":"The helium atom has 2 protons in the nucleus and 2 electrons."},{"Start":"02:16.085 ","End":"02:18.380","Text":"Of course, it also has 2 neutrons,"},{"Start":"02:18.380 ","End":"02:20.180","Text":"but these are less important."},{"Start":"02:20.180 ","End":"02:23.960","Text":"Now, each electron is attracted to the nucleus,"},{"Start":"02:23.960 ","End":"02:27.230","Text":"but in addition, the 2 electrons repel each other."},{"Start":"02:27.230 ","End":"02:28.895","Text":"We can draw it like this."},{"Start":"02:28.895 ","End":"02:32.270","Text":"Here\u0027s our nucleus, positively charged."},{"Start":"02:32.270 ","End":"02:35.450","Text":"Here\u0027s our negatively charged electron,"},{"Start":"02:35.450 ","End":"02:38.255","Text":"and another negatively charged electron."},{"Start":"02:38.255 ","End":"02:44.065","Text":"Each electron is attracted to the nucleus."},{"Start":"02:44.065 ","End":"02:51.600","Text":"But in addition, there is repulsion between the 2 electrons."},{"Start":"02:51.600 ","End":"02:53.485","Text":"That\u0027s what makes all the difference,"},{"Start":"02:53.485 ","End":"02:58.450","Text":"is the repulsion between the electrons that alters the energies."},{"Start":"02:58.450 ","End":"03:00.880","Text":"If we don\u0027t include the repulsion,"},{"Start":"03:00.880 ","End":"03:06.160","Text":"the energy of each electron would be just as in the hydrogen like atom."},{"Start":"03:06.160 ","End":"03:12.340","Text":"The energy of electron in shell n would be minus R_H,"},{"Start":"03:12.340 ","End":"03:15.595","Text":"that\u0027s Rydberg constant times Z^2,"},{"Start":"03:15.595 ","End":"03:20.530","Text":"Z is the nuclear charge divided by n^2,"},{"Start":"03:20.530 ","End":"03:23.035","Text":"where n is the principal quantum number."},{"Start":"03:23.035 ","End":"03:25.465","Text":"Now supposing we\u0027re considering helium,"},{"Start":"03:25.465 ","End":"03:27.305","Text":"then Z is 2."},{"Start":"03:27.305 ","End":"03:31.075","Text":"Supposing we want the ground state where n is equal to one,"},{"Start":"03:31.075 ","End":"03:35.665","Text":"then we get E_1 is equal to minus 4R_H,"},{"Start":"03:35.665 ","End":"03:38.620","Text":"because Z is 2, that\u0027s 2^2."},{"Start":"03:38.620 ","End":"03:41.085","Text":"4 is 1, that\u0027s 1."},{"Start":"03:41.085 ","End":"03:44.635","Text":"So we have E_1 equal to minus 4R_H."},{"Start":"03:44.635 ","End":"03:50.120","Text":"Now this energy is much lower than the experimentally measured energy."},{"Start":"03:50.120 ","End":"03:53.270","Text":"If we include the electron-electron repulsion,"},{"Start":"03:53.270 ","End":"03:55.445","Text":"the energy will be higher."},{"Start":"03:55.445 ","End":"03:57.845","Text":"In other words, it won\u0027t be so negative."},{"Start":"03:57.845 ","End":"04:01.130","Text":"One of the ways of writing this is to consider"},{"Start":"04:01.130 ","End":"04:04.520","Text":"that the such a thing as effective nuclear charge,"},{"Start":"04:04.520 ","End":"04:09.580","Text":"as if the electron doesn\u0027t feel the full charge of Z equals 2."},{"Start":"04:09.580 ","End":"04:13.490","Text":"Then we can write very approximately E_n is equal to"},{"Start":"04:13.490 ","End":"04:19.085","Text":"minus R_HZ effective squared divided by n^2."},{"Start":"04:19.085 ","End":"04:22.850","Text":"Call this Z effective as effective atomic number."},{"Start":"04:22.850 ","End":"04:26.330","Text":"Now if we compare this equation with"},{"Start":"04:26.330 ","End":"04:30.410","Text":"the experimentally measured energy of an electron in helium,"},{"Start":"04:30.410 ","End":"04:35.150","Text":"will discover that Z effective lies between 1,"},{"Start":"04:35.150 ","End":"04:37.220","Text":"which is appropriate for hydrogen,"},{"Start":"04:37.220 ","End":"04:39.905","Text":"and 2 which is appropriate for helium."},{"Start":"04:39.905 ","End":"04:42.335","Text":"So it\u0027s less than 2,"},{"Start":"04:42.335 ","End":"04:44.090","Text":"but greater than 1."},{"Start":"04:44.090 ","End":"04:47.090","Text":"Now, it\u0027s often said that"},{"Start":"04:47.090 ","End":"04:51.405","Text":"the electrons shield each other from the full effect of the nucleus."},{"Start":"04:51.405 ","End":"04:56.740","Text":"That\u0027s the reason why Z effective is less than the true value of Z."},{"Start":"04:56.740 ","End":"05:00.875","Text":"Of course, the real reason for Z effective not"},{"Start":"05:00.875 ","End":"05:05.240","Text":"being less than Z is that there is electron-electron repulsion,"},{"Start":"05:05.240 ","End":"05:08.420","Text":"but it\u0027s very convenient to talk about shielding."},{"Start":"05:08.420 ","End":"05:12.770","Text":"We\u0027re going to compare penetration with shielding."},{"Start":"05:12.770 ","End":"05:16.520","Text":"Will see the penetration causes shooting."},{"Start":"05:16.520 ","End":"05:20.554","Text":"The closer the orbital containing the electron is to the nucleus,"},{"Start":"05:20.554 ","End":"05:22.429","Text":"the more the electric fields,"},{"Start":"05:22.429 ","End":"05:24.410","Text":"the attraction to the nucleus."},{"Start":"05:24.410 ","End":"05:28.075","Text":"So we get a higher value of Z effective,"},{"Start":"05:28.075 ","End":"05:31.535","Text":"and the less shielded from the nucleus."},{"Start":"05:31.535 ","End":"05:38.089","Text":"Now, all the radio wave functions overlap because it\u0027s a probability,"},{"Start":"05:38.089 ","End":"05:41.855","Text":"and the probability changes with the distance from the nucleus,"},{"Start":"05:41.855 ","End":"05:44.825","Text":"but some penetrate closer to the nucleus."},{"Start":"05:44.825 ","End":"05:49.220","Text":"We saw that all the s orbitals penetrate very close to the nucleus."},{"Start":"05:49.220 ","End":"05:53.809","Text":"So they are less shielded from the nucleus and are lower in energy."},{"Start":"05:53.809 ","End":"05:56.180","Text":"If we consider penetration,"},{"Start":"05:56.180 ","End":"05:58.490","Text":"we can understand shooting."},{"Start":"05:58.490 ","End":"06:01.955","Text":"Now if we look at plots of the radial distribution function,"},{"Start":"06:01.955 ","End":"06:08.045","Text":"you may remember we drew this in a previous video for the 1s orbital."},{"Start":"06:08.045 ","End":"06:10.795","Text":"You may recall that P\u0026L,"},{"Start":"06:10.795 ","End":"06:13.120","Text":"which has a radial distribution function,"},{"Start":"06:13.120 ","End":"06:14.680","Text":"is equal to r squared,"},{"Start":"06:14.680 ","End":"06:20.275","Text":"the distance from the nucleus times radio wave function^2."},{"Start":"06:20.275 ","End":"06:24.385","Text":"Then if we do that for all 1s, 2s, and 3s,"},{"Start":"06:24.385 ","End":"06:28.390","Text":"we find that the 1s orbital penetrates more than 2s,"},{"Start":"06:28.390 ","End":"06:31.360","Text":"and 2s penetrates more than 3s."},{"Start":"06:31.360 ","End":"06:38.605","Text":"So the order of the energies is 1s is a lower energy than 2s, then of 3s."},{"Start":"06:38.605 ","End":"06:48.370","Text":"In other words, we can say that 1s fields are higher Z effective than 2s."},{"Start":"07:00.200 ","End":"07:05.900","Text":"Now we can also compare orbitals other than the s orbital."},{"Start":"07:05.900 ","End":"07:08.920","Text":"If we can understand it as L increases,"},{"Start":"07:08.920 ","End":"07:12.145","Text":"as the angular momentum increases,"},{"Start":"07:12.145 ","End":"07:14.875","Text":"the electron is thrown further from the nucleus."},{"Start":"07:14.875 ","End":"07:20.815","Text":"The 3s penetrates more than 3p and 3p penetrates more than 3d."},{"Start":"07:20.815 ","End":"07:25.985","Text":"Then the order of the energies of electrons in these orbitals is 3s less,"},{"Start":"07:25.985 ","End":"07:29.740","Text":"lower than 3p, lower than 3D."},{"Start":"07:29.740 ","End":"07:35.980","Text":"So we can say that electron and 3D is shielded more than in 3p,"},{"Start":"07:35.980 ","End":"07:39.955","Text":"which has shielded more than one in 3s."},{"Start":"07:39.955 ","End":"07:45.960","Text":"We can say again that the Z effective for"},{"Start":"07:45.960 ","End":"07:51.855","Text":"3s is greater than Z effective for 3p,"},{"Start":"07:51.855 ","End":"07:56.395","Text":"which is greater than Z effective for 3d."},{"Start":"07:56.395 ","End":"07:58.010","Text":"So in this video,"},{"Start":"07:58.010 ","End":"08:02.670","Text":"we introduced the multielectron atoms."}],"ID":20952},{"Watched":false,"Name":"Electron Configurations Rules","Duration":"7m 34s","ChapterTopicVideoID":20170,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20170.jpeg","UploadDate":"2019-08-15T02:36:53.4730000","DurationForVideoObject":"PT7M34S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.530","Text":"In the previous video,"},{"Start":"00:01.530 ","End":"00:04.365","Text":"we introduced multi-electron atoms."},{"Start":"00:04.365 ","End":"00:09.780","Text":"In this video, we\u0027ll discuss the electronic configuration of these atoms."},{"Start":"00:09.780 ","End":"00:13.020","Text":"The electron configuration of an atom is"},{"Start":"00:13.020 ","End":"00:16.495","Text":"the distribution of electrons amongst the orbitals."},{"Start":"00:16.495 ","End":"00:20.490","Text":"Now, in order to distribute the electrons amongst the orbitals,"},{"Start":"00:20.490 ","End":"00:22.020","Text":"we need rules,"},{"Start":"00:22.020 ","End":"00:26.825","Text":"which had been developed both experimentally, and theoretically."},{"Start":"00:26.825 ","End":"00:29.630","Text":"The first rule is that electrons occupy"},{"Start":"00:29.630 ","End":"00:33.370","Text":"the orbitals so as to minimize the energy of the atom."},{"Start":"00:33.370 ","End":"00:37.670","Text":"The order in which the orbitals are filled has been determined experimentally,"},{"Start":"00:37.670 ","End":"00:39.760","Text":"and here it is: 1s,"},{"Start":"00:39.760 ","End":"00:41.155","Text":"then 2s, 2p,"},{"Start":"00:41.155 ","End":"00:43.105","Text":"3s, 3p, 4s,"},{"Start":"00:43.105 ","End":"00:44.575","Text":"3d, 4p,"},{"Start":"00:44.575 ","End":"00:47.590","Text":"5s, 4d, 5p, 6s,"},{"Start":"00:47.590 ","End":"00:50.395","Text":"4f, 5d, 6p,"},{"Start":"00:50.395 ","End":"00:54.360","Text":"7s, 5f, 6d, and then 7p."},{"Start":"00:54.360 ","End":"00:55.980","Text":"In the periodic table,"},{"Start":"00:55.980 ","End":"00:59.255","Text":"these are all the orbitals that have electrons."},{"Start":"00:59.255 ","End":"01:02.285","Text":"Now, somewhat difficult to remember this order,"},{"Start":"01:02.285 ","End":"01:04.190","Text":"so here\u0027s a way that\u0027s easier."},{"Start":"01:04.190 ","End":"01:08.416","Text":"We write out the orbitals like this, these rows,"},{"Start":"01:08.416 ","End":"01:15.290","Text":"and then we use straight diagonal lines to connect them."},{"Start":"01:15.290 ","End":"01:17.205","Text":"We start with 1s,"},{"Start":"01:17.205 ","End":"01:21.460","Text":"then 2s, then 2p, 3s,"},{"Start":"01:21.460 ","End":"01:25.240","Text":"then 3p,4s, then 3d, 4p,"},{"Start":"01:25.240 ","End":"01:31.325","Text":"5s, and then 4d, 5p, 6s."},{"Start":"01:31.325 ","End":"01:36.400","Text":"Then 4f, 5d, 6p, 7s."},{"Start":"01:36.400 ","End":"01:39.650","Text":"Then finally 5f, 6d, 7p."},{"Start":"01:39.970 ","End":"01:46.630","Text":"That gives us more or less the order in which electrons fill the orbitals."},{"Start":"01:46.630 ","End":"01:50.765","Text":"Now, the second rule is Pauli exclusion principle."},{"Start":"01:50.765 ","End":"01:57.865","Text":"This says that no 2 electrons in an atom can have the same 4 quantum numbers."},{"Start":"01:57.865 ","End":"02:01.295","Text":"So if we have 2 electrons in the same orbital,"},{"Start":"02:01.295 ","End":"02:03.560","Text":"that means they have the same n,"},{"Start":"02:03.560 ","End":"02:05.640","Text":"l, and m_l,"},{"Start":"02:05.640 ","End":"02:09.855","Text":"then we already have 3 quantum numbers that are the same."},{"Start":"02:09.855 ","End":"02:13.305","Text":"So the fourth one, m_s must be different."},{"Start":"02:13.305 ","End":"02:17.745","Text":"One must be m_s equal to plus a half,"},{"Start":"02:17.745 ","End":"02:19.485","Text":"that\u0027s what\u0027s the spin up,"},{"Start":"02:19.485 ","End":"02:23.210","Text":"and the other ms equal to minus half of the spin down."},{"Start":"02:23.210 ","End":"02:25.100","Text":"So they have opposite spins,"},{"Start":"02:25.100 ","End":"02:26.385","Text":"1 up and 1 down,"},{"Start":"02:26.385 ","End":"02:28.695","Text":"and we say they are paired."},{"Start":"02:28.695 ","End":"02:30.425","Text":"We can draw it like this,"},{"Start":"02:30.425 ","End":"02:33.425","Text":"or sometimes for short, like this."},{"Start":"02:33.425 ","End":"02:39.335","Text":"Now, there are important consequences to this Pauli exclusion principle."},{"Start":"02:39.335 ","End":"02:44.135","Text":"For example, if we have a sub-shell with a particular value of l,"},{"Start":"02:44.135 ","End":"02:50.119","Text":"that we can work out how many electrons can fill the sub-shell."},{"Start":"02:50.119 ","End":"02:55.520","Text":"We know if the sub-shell has a particular value of l,"},{"Start":"02:55.520 ","End":"02:59.450","Text":"then there are 2l plus 1 orbitals."},{"Start":"02:59.450 ","End":"03:03.095","Text":"If each orbital can take 2 electrons at most,"},{"Start":"03:03.095 ","End":"03:11.845","Text":"then the maximum number of electrons that can fill this l sub-shell is 2 times 2l plus 1."},{"Start":"03:11.845 ","End":"03:17.660","Text":"So 2 times 2l plus 1 is the maximum number of electrons in a sub-shell."},{"Start":"03:17.660 ","End":"03:20.630","Text":"Let\u0027s try various cases."},{"Start":"03:20.630 ","End":"03:22.115","Text":"If we have s,"},{"Start":"03:22.115 ","End":"03:24.845","Text":"that means l is equal to 0,"},{"Start":"03:24.845 ","End":"03:27.920","Text":"then 2 times 2l plus 1 is just 2,"},{"Start":"03:27.920 ","End":"03:32.500","Text":"so we have 2 electrons in the s orbital."},{"Start":"03:32.500 ","End":"03:36.270","Text":"Now, supposing that we have the p subshell,"},{"Start":"03:36.270 ","End":"03:38.775","Text":"that means l is equal to 1,"},{"Start":"03:38.775 ","End":"03:41.565","Text":"and there are 3 orbitals,"},{"Start":"03:41.565 ","End":"03:42.705","Text":"2l plus 1,"},{"Start":"03:42.705 ","End":"03:48.280","Text":"3 orbitals, and then we can have a maximum of 6 electrons."},{"Start":"03:48.280 ","End":"03:52.140","Text":"Now, supposing we have the d subshell."},{"Start":"03:52.140 ","End":"03:55.455","Text":"For d, l is equal to 2."},{"Start":"03:55.455 ","End":"04:01.900","Text":"That means there are 5 orbitals, and 10 electrons."},{"Start":"04:01.900 ","End":"04:03.650","Text":"This is very important,"},{"Start":"04:03.650 ","End":"04:08.629","Text":"so we can have a maximum of 2 electrons in the s subshell,"},{"Start":"04:08.629 ","End":"04:11.345","Text":"6 electrons in the p subshell,"},{"Start":"04:11.345 ","End":"04:13.885","Text":"and 10 in the d subshell."},{"Start":"04:13.885 ","End":"04:18.755","Text":"Here\u0027s an example, supposing we have a full p subshell,"},{"Start":"04:18.755 ","End":"04:21.965","Text":"how can we put in the 6 electrons?"},{"Start":"04:21.965 ","End":"04:24.845","Text":"2 in 1 of the p orbitals,"},{"Start":"04:24.845 ","End":"04:26.755","Text":"2 in the next 1,"},{"Start":"04:26.755 ","End":"04:29.145","Text":"and 2 in the third 1,"},{"Start":"04:29.145 ","End":"04:31.570","Text":"a total of 6."},{"Start":"04:31.570 ","End":"04:34.895","Text":"The third rule is Hund\u0027s Rule."},{"Start":"04:34.895 ","End":"04:38.900","Text":"It says that when degenerate orbitals that are available,"},{"Start":"04:38.900 ","End":"04:43.010","Text":"the electrons fill them singly with parallel spins."},{"Start":"04:43.010 ","End":"04:46.235","Text":"That this is the lowest energy configuration."},{"Start":"04:46.235 ","End":"04:48.650","Text":"It\u0027s a bit like a bus."},{"Start":"04:48.650 ","End":"04:50.330","Text":"When people go into the bus,"},{"Start":"04:50.330 ","End":"04:54.090","Text":"they tend to sit in different seats."},{"Start":"04:55.820 ","End":"04:59.645","Text":"Then only when all the single seats are filled up,"},{"Start":"04:59.645 ","End":"05:01.730","Text":"then somebody else can come in,"},{"Start":"05:01.730 ","End":"05:03.320","Text":"and sit beside them."},{"Start":"05:03.320 ","End":"05:05.330","Text":"Let\u0027s take an example."},{"Start":"05:05.330 ","End":"05:08.720","Text":"Supposing we want to fill the p orbitals,"},{"Start":"05:08.720 ","End":"05:11.585","Text":"we have 3 degenerate p orbitals."},{"Start":"05:11.585 ","End":"05:15.270","Text":"The first electron will go in the first one,"},{"Start":"05:15.270 ","End":"05:17.685","Text":"the second, second one,"},{"Start":"05:17.685 ","End":"05:19.825","Text":"third one into the third one."},{"Start":"05:19.825 ","End":"05:23.540","Text":"But the fourth will then go in to the first one,"},{"Start":"05:23.540 ","End":"05:25.535","Text":"the fifth into the second,"},{"Start":"05:25.535 ","End":"05:28.570","Text":"and the sixth into the third."},{"Start":"05:28.570 ","End":"05:34.400","Text":"Now, we have 3 pairs of electrons."},{"Start":"05:34.400 ","End":"05:38.060","Text":"How quick can we write these electron configurations?"},{"Start":"05:38.060 ","End":"05:41.165","Text":"We call it representing electron configurations."},{"Start":"05:41.165 ","End":"05:44.705","Text":"It turns out that there is more than 1 method."},{"Start":"05:44.705 ","End":"05:46.700","Text":"Let\u0027s take an example."},{"Start":"05:46.700 ","End":"05:48.395","Text":"Supposing we have carbon."},{"Start":"05:48.395 ","End":"05:50.780","Text":"For, carbon z is equal to 6,"},{"Start":"05:50.780 ","End":"05:54.290","Text":"so 6 protons, and 6 electrons."},{"Start":"05:54.290 ","End":"05:57.575","Text":"The first 2 electrons in the 1s orbital,"},{"Start":"05:57.575 ","End":"06:00.180","Text":"the second 2 in the 2s,"},{"Start":"06:00.180 ","End":"06:05.085","Text":"and the third pair into 2p."},{"Start":"06:05.085 ","End":"06:08.270","Text":"Now, we\u0027ve distributed all 6 electrons."},{"Start":"06:08.270 ","End":"06:14.045","Text":"Sometimes this is called spdf method."},{"Start":"06:14.045 ","End":"06:18.720","Text":"Now, we may want to expand our description,"},{"Start":"06:18.720 ","End":"06:23.500","Text":"and say precisely in which p orbitals we are putting the electrons."},{"Start":"06:23.500 ","End":"06:29.185","Text":"We saw from Hund that you put in each electron singly."},{"Start":"06:29.185 ","End":"06:32.775","Text":"We have 2 electrons in 1s,"},{"Start":"06:32.775 ","End":"06:34.694","Text":"2 electrons in 2s,"},{"Start":"06:34.694 ","End":"06:36.870","Text":"1 electron, say,"},{"Start":"06:36.870 ","End":"06:39.835","Text":"in p_x, and 1 in p_y."},{"Start":"06:39.835 ","End":"06:42.620","Text":"It doesn\u0027t matter where they are right here, x, y,"},{"Start":"06:42.620 ","End":"06:47.255","Text":"or z, because all these orbitals have the same energy."},{"Start":"06:47.255 ","End":"06:53.585","Text":"So this is a more expanded form of the spdf description."},{"Start":"06:53.585 ","End":"06:57.380","Text":"Now, we can do something even more detailed."},{"Start":"06:57.380 ","End":"07:02.495","Text":"We can draw squares for each orbital as we did before."},{"Start":"07:02.495 ","End":"07:04.460","Text":"If we have 1s orbital,"},{"Start":"07:04.460 ","End":"07:06.230","Text":"we have 2 electrons,"},{"Start":"07:06.230 ","End":"07:09.350","Text":"2s we have 2 electrons,"},{"Start":"07:09.350 ","End":"07:14.540","Text":"2p we have 1 here and 1 here."},{"Start":"07:14.540 ","End":"07:21.559","Text":"We can put them in any 2 of the orbitals as long as the spins are parallel."},{"Start":"07:21.559 ","End":"07:27.205","Text":"In this video, we learned about the rules that govern electron configurations."},{"Start":"07:27.205 ","End":"07:28.535","Text":"In the next video,"},{"Start":"07:28.535 ","End":"07:33.840","Text":"we\u0027ll actually apply these rules to all the elements."}],"ID":20945},{"Watched":false,"Name":"Electron Configurations Aufbau Process","Duration":"9m ","ChapterTopicVideoID":20171,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20171.jpeg","UploadDate":"2019-08-15T02:38:30.7430000","DurationForVideoObject":"PT9M","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.785","Text":"In the previous video,"},{"Start":"00:01.785 ","End":"00:05.760","Text":"we learned about the rules that govern electron configurations."},{"Start":"00:05.760 ","End":"00:09.525","Text":"In this video, we will show how to apply these rules."},{"Start":"00:09.525 ","End":"00:17.190","Text":"We begin by defining the Aufbau process as a process by which we obtain all the elements."},{"Start":"00:17.190 ","End":"00:20.850","Text":"Now, Aufbau is a German word for building up."},{"Start":"00:20.850 ","End":"00:25.515","Text":"The Aufbau process is the way we build up the periodic table."},{"Start":"00:25.515 ","End":"00:29.280","Text":"We begin with Z=1 and add another electron to obtain"},{"Start":"00:29.280 ","End":"00:35.855","Text":"the electron configuration for Z=2 and so on until we\u0027ve completed all the elements."},{"Start":"00:35.855 ","End":"00:40.055","Text":"Now just to remind you of the order in which the orbitals are filled,"},{"Start":"00:40.055 ","End":"00:43.535","Text":"we had this in the previous video. Here\u0027s the order."},{"Start":"00:43.535 ","End":"00:46.925","Text":"Let\u0027s begin with the 1st period where n=1."},{"Start":"00:46.925 ","End":"00:50.390","Text":"This is the 1st row in the periodic table."},{"Start":"00:50.390 ","End":"00:53.920","Text":"N=1 there is only the 1s orbital."},{"Start":"00:53.920 ","End":"00:55.915","Text":"We begin with Z=1,"},{"Start":"00:55.915 ","End":"00:57.994","Text":"which of course is hydrogen,"},{"Start":"00:57.994 ","End":"01:00.890","Text":"and we\u0027re putting 1 electron into the 1s orbitals."},{"Start":"01:00.890 ","End":"01:02.845","Text":"Here\u0027s 1s, 1 electron."},{"Start":"01:02.845 ","End":"01:04.290","Text":"Then we go on to helium,"},{"Start":"01:04.290 ","End":"01:05.805","Text":"which is Z=2,"},{"Start":"01:05.805 ","End":"01:08.850","Text":"and there are 2 electrons in the 1s orbital,"},{"Start":"01:08.850 ","End":"01:12.390","Text":"a pair of electrons and that of course is a rare gas."},{"Start":"01:12.390 ","End":"01:14.745","Text":"Helium is the first rare gas."},{"Start":"01:14.745 ","End":"01:19.715","Text":"Now we go to the 2nd row of the periodic table where n=2."},{"Start":"01:19.715 ","End":"01:22.340","Text":"The first one we fill in is 2s,"},{"Start":"01:22.340 ","End":"01:24.590","Text":"the first orbital is 2s."},{"Start":"01:24.590 ","End":"01:29.070","Text":"Here we have it Z=3, that\u0027s lithium."},{"Start":"01:29.070 ","End":"01:33.200","Text":"We have 2 electrons in 1s and 1 electron in 2s."},{"Start":"01:33.200 ","End":"01:37.850","Text":"Or another way of writing this is helium in square brackets."},{"Start":"01:37.850 ","End":"01:43.610","Text":"The same electron configuration as helium has then 1 electron in 2s,"},{"Start":"01:43.610 ","End":"01:45.740","Text":"and Z=4 is beryllium,"},{"Start":"01:45.740 ","End":"01:47.465","Text":"2 electrons in 1s,"},{"Start":"01:47.465 ","End":"01:48.920","Text":"2 in 2s,"},{"Start":"01:48.920 ","End":"01:52.160","Text":"or again, helium square brackets,"},{"Start":"01:52.160 ","End":"01:54.480","Text":"then 2 electrons in 2s."},{"Start":"01:54.480 ","End":"01:57.255","Text":"Here we filled up 2s."},{"Start":"01:57.255 ","End":"02:01.340","Text":"Now the next orbital to be filled up is 2p."},{"Start":"02:01.340 ","End":"02:04.450","Text":"We go 1s2s2p."},{"Start":"02:04.450 ","End":"02:09.935","Text":"Now we\u0027re going to fill in all of 2p and we start off with boron,"},{"Start":"02:09.935 ","End":"02:13.220","Text":"which has the same configuration as helium,"},{"Start":"02:13.220 ","End":"02:16.500","Text":"then 2 electrons in 2s and 1 in 2p."},{"Start":"02:16.500 ","End":"02:18.545","Text":"So 2 in 2s,"},{"Start":"02:18.545 ","End":"02:22.680","Text":"here\u0027s 2p, 1 in 2p."},{"Start":"02:22.680 ","End":"02:27.275","Text":"Then we go right along the 2nd period."},{"Start":"02:27.275 ","End":"02:30.690","Text":"Carbon has 2 electrons in 2p,"},{"Start":"02:30.690 ","End":"02:34.735","Text":"then nitrogen has 3,"},{"Start":"02:34.735 ","End":"02:38.955","Text":"and then oxygen has 4 starting to pair them."},{"Start":"02:38.955 ","End":"02:40.980","Text":"Fluorine has 5,"},{"Start":"02:40.980 ","End":"02:43.440","Text":"and neon has 6."},{"Start":"02:43.440 ","End":"02:46.350","Text":"Neon is again a rare gas."},{"Start":"02:46.350 ","End":"02:53.440","Text":"The configuration of neon is helium, 2s^2, 2p^6."},{"Start":"02:53.440 ","End":"02:55.610","Text":"Now we go on to the 3rd period,"},{"Start":"02:55.610 ","End":"02:57.560","Text":"the 3rd row in the periodic table,"},{"Start":"02:57.560 ","End":"03:01.540","Text":"where the principal quantum number at the beginning is n=3."},{"Start":"03:01.540 ","End":"03:05.235","Text":"We\u0027re going to fill in first the 3s."},{"Start":"03:05.235 ","End":"03:08.745","Text":"We\u0027ll start with Z=11, which is sodium."},{"Start":"03:08.745 ","End":"03:12.435","Text":"That\u0027s like neon, the previous rare gas,"},{"Start":"03:12.435 ","End":"03:14.130","Text":"1 electron in 3s."},{"Start":"03:14.130 ","End":"03:17.880","Text":"We go all the way along to Z=18,"},{"Start":"03:17.880 ","End":"03:20.040","Text":"which is argon,"},{"Start":"03:20.040 ","End":"03:21.705","Text":"which is like neon,"},{"Start":"03:21.705 ","End":"03:23.790","Text":"with 2 electrons in 3s,"},{"Start":"03:23.790 ","End":"03:25.815","Text":"6 electrons in 3p,"},{"Start":"03:25.815 ","End":"03:28.325","Text":"and argon is a rare gas."},{"Start":"03:28.325 ","End":"03:31.040","Text":"Now we\u0027ve completed the 3rd period."},{"Start":"03:31.040 ","End":"03:34.760","Text":"Now we go to the 4th period with n=4."},{"Start":"03:34.760 ","End":"03:37.385","Text":"We start off with Z=19."},{"Start":"03:37.385 ","End":"03:42.140","Text":"That\u0027s potassium is like argon and 1 electron in 4s."},{"Start":"03:42.140 ","End":"03:47.705","Text":"Then we go to the next one, which is calcium,"},{"Start":"03:47.705 ","End":"03:52.265","Text":"that\u0027s Z=20 and now we have 2 electrons and 4s,"},{"Start":"03:52.265 ","End":"03:55.549","Text":"so 1 for potassium 2 for calcium."},{"Start":"03:55.549 ","End":"04:00.270","Text":"Now after 4s, we\u0027d go to 3d."},{"Start":"04:00.270 ","End":"04:02.220","Text":"We have to fill up 3d."},{"Start":"04:02.220 ","End":"04:06.915","Text":"We begin with scandium that\u0027s Z=21."},{"Start":"04:06.915 ","End":"04:12.450","Text":"It\u0027s like argon, 2 electrons in 4s and 1 electron in 3d."},{"Start":"04:12.450 ","End":"04:16.815","Text":"We go all the way along to Z=30 that\u0027s zinc,"},{"Start":"04:16.815 ","End":"04:18.434","Text":"which is like argon,"},{"Start":"04:18.434 ","End":"04:20.070","Text":"2 electrons in 4s,"},{"Start":"04:20.070 ","End":"04:25.140","Text":"and 10 electrons in 3d that fills up 3d."},{"Start":"04:25.140 ","End":"04:28.020","Text":"How do we fill up the 3d orbitals?"},{"Start":"04:28.020 ","End":"04:29.325","Text":"We had, of course,"},{"Start":"04:29.325 ","End":"04:31.307","Text":"2 electrons in 4s."},{"Start":"04:31.307 ","End":"04:38.925","Text":"Then 3d we fill up according to Hund 1, 2,"},{"Start":"04:38.925 ","End":"04:41.760","Text":"3, 4, 5,"},{"Start":"04:41.760 ","End":"04:44.040","Text":"and then start to pair 1,"},{"Start":"04:44.040 ","End":"04:47.750","Text":"2, 3, 4, 5."},{"Start":"04:47.750 ","End":"04:49.970","Text":"That\u0027s what we have for zinc."},{"Start":"04:49.970 ","End":"04:52.430","Text":"Now there are exceptions."},{"Start":"04:52.430 ","End":"04:58.475","Text":"There are 2 exceptions, Z=24 and Z=29."},{"Start":"04:58.475 ","End":"05:01.955","Text":"That\u0027s chromium and copper."},{"Start":"05:01.955 ","End":"05:04.970","Text":"Now, let\u0027s start off with chromium."},{"Start":"05:04.970 ","End":"05:06.725","Text":"It\u0027s like argon."},{"Start":"05:06.725 ","End":"05:14.220","Text":"Then 1 electron in 4s and 5 electrons in 3d."},{"Start":"05:17.050 ","End":"05:22.360","Text":"There\u0027s a special stability to half-full orbitals."},{"Start":"05:22.360 ","End":"05:24.760","Text":"We have half-full subshells,"},{"Start":"05:24.760 ","End":"05:28.675","Text":"where 1 in 4s and 5 electrons in 3d,"},{"Start":"05:28.675 ","End":"05:31.920","Text":"so it\u0027s a half-full subshell."},{"Start":"05:31.920 ","End":"05:33.625","Text":"Then we get to copper."},{"Start":"05:33.625 ","End":"05:35.304","Text":"Copper is the other exception."},{"Start":"05:35.304 ","End":"05:37.765","Text":"It still has 1 electron in 4s,"},{"Start":"05:37.765 ","End":"05:41.500","Text":"but now it has 10 electrons in 3d."},{"Start":"05:41.500 ","End":"05:44.180","Text":"There are 5 pairs."},{"Start":"05:46.490 ","End":"05:51.255","Text":"Now, after we filled up 4s and 3d,"},{"Start":"05:51.255 ","End":"05:53.460","Text":"we go back to 4p."},{"Start":"05:53.460 ","End":"05:56.235","Text":"There\u0027s 2 electrons in 4s, 10 in 3d,"},{"Start":"05:56.235 ","End":"06:02.075","Text":"and now we go to 4p We begin with 1 electron in 4p, that\u0027s aluminum."},{"Start":"06:02.075 ","End":"06:07.025","Text":"Fill up all of the 4p orbitals till we get Z=36,"},{"Start":"06:07.025 ","End":"06:09.295","Text":"which is now 4p^6,"},{"Start":"06:09.295 ","End":"06:14.014","Text":"and that\u0027s krypton, which is yet another rare gas."},{"Start":"06:14.014 ","End":"06:17.830","Text":"Now we have 6 electrons and 4p."},{"Start":"06:17.830 ","End":"06:22.525","Text":"Now we get to the 5th period, n=5."},{"Start":"06:22.525 ","End":"06:25.250","Text":"That begins with rubidium,"},{"Start":"06:25.250 ","End":"06:26.494","Text":"which is like krypton,"},{"Start":"06:26.494 ","End":"06:28.295","Text":"the previous rare gas,"},{"Start":"06:28.295 ","End":"06:32.060","Text":"and 1 electron in 5s, that\u0027s Z=37."},{"Start":"06:32.060 ","End":"06:35.890","Text":"Then we fill in 4d,"},{"Start":"06:35.890 ","End":"06:40.650","Text":"and then 5p so we end up with xenon,"},{"Start":"06:40.650 ","End":"06:42.240","Text":"which is like krypton,"},{"Start":"06:42.240 ","End":"06:44.220","Text":"has 10 electrons in 4d,"},{"Start":"06:44.220 ","End":"06:47.095","Text":"2 and 5s, and 6 and 5p,"},{"Start":"06:47.095 ","End":"06:49.745","Text":"and that\u0027s again a rare gas."},{"Start":"06:49.745 ","End":"06:53.375","Text":"The 5th period is rather similar to the 4th period."},{"Start":"06:53.375 ","End":"06:55.460","Text":"Now we get to the 6th period,"},{"Start":"06:55.460 ","End":"06:56.885","Text":"which is a bit different."},{"Start":"06:56.885 ","End":"06:58.745","Text":"That\u0027s n=6."},{"Start":"06:58.745 ","End":"07:01.865","Text":"We start off with cesium,"},{"Start":"07:01.865 ","End":"07:03.817","Text":"which is like xenon,"},{"Start":"07:03.817 ","End":"07:05.665","Text":"1 electron, and 6s."},{"Start":"07:05.665 ","End":"07:12.125","Text":"We fill up 6s and we get to Z=57, which is lanthanum."},{"Start":"07:12.125 ","End":"07:15.070","Text":"Now lanthanum is like xenon,"},{"Start":"07:15.070 ","End":"07:17.205","Text":"2 electrons in 6s,"},{"Start":"07:17.205 ","End":"07:20.120","Text":"and although according to the list we had,"},{"Start":"07:20.120 ","End":"07:22.970","Text":"we should now put electrons into 4f."},{"Start":"07:22.970 ","End":"07:27.800","Text":"It turns out that 4f and 5d have very similar energies."},{"Start":"07:27.800 ","End":"07:31.265","Text":"Sometimes one is greater than the other, sometimes the other."},{"Start":"07:31.265 ","End":"07:33.185","Text":"In this case, for lanthanum,"},{"Start":"07:33.185 ","End":"07:38.360","Text":"5d is a little lower in energy than 4f so we put 1 electron into 5d,"},{"Start":"07:38.360 ","End":"07:40.730","Text":"and this is the first lanthanide,"},{"Start":"07:40.730 ","End":"07:44.420","Text":"and these lanthanides are written at the bottom of the periodic table."},{"Start":"07:44.420 ","End":"07:46.355","Text":"We\u0027ll see that in the next video."},{"Start":"07:46.355 ","End":"07:51.480","Text":"Now, the one after lanthanum is cerium,"},{"Start":"07:51.480 ","End":"07:55.560","Text":"and that\u0027s like xenon 6s^2, 4f^2."},{"Start":"07:55.560 ","End":"07:59.094","Text":"We\u0027re putting 2 electrons instead of 1 and 5d,"},{"Start":"07:59.094 ","End":"08:02.180","Text":"we\u0027re putting 2 into 4f."},{"Start":"08:02.180 ","End":"08:07.500","Text":"Then we\u0027re going to fill up all the f orbitals and also 1 and 5d,"},{"Start":"08:07.500 ","End":"08:09.680","Text":"and that\u0027s the last of the lanthanides,"},{"Start":"08:09.680 ","End":"08:11.135","Text":"it\u0027s called a tissue."},{"Start":"08:11.135 ","End":"08:19.095","Text":"Then we have to go and fill in all the 5d and then all the 6p till we get to the end,"},{"Start":"08:19.095 ","End":"08:23.700","Text":"and that\u0027s radon, which is yet another rare gas,"},{"Start":"08:25.190 ","End":"08:27.450","Text":"and it\u0027s like xenon."},{"Start":"08:27.450 ","End":"08:28.950","Text":"We filled up 6s,"},{"Start":"08:28.950 ","End":"08:30.360","Text":"filled up 4f,"},{"Start":"08:30.360 ","End":"08:33.490","Text":"filled up 5d, filled up 6p."},{"Start":"08:33.490 ","End":"08:36.890","Text":"Then we get to the 7th and final period,"},{"Start":"08:36.890 ","End":"08:39.290","Text":"which includes the actinides."},{"Start":"08:39.290 ","End":"08:41.225","Text":"These like the lanthanides,"},{"Start":"08:41.225 ","End":"08:44.704","Text":"are written at the bottom of the periodic table."},{"Start":"08:44.704 ","End":"08:49.295","Text":"There we fill in the 5f orbitals,"},{"Start":"08:49.295 ","End":"08:53.870","Text":"and many of these are radioactive as is radon."},{"Start":"08:53.870 ","End":"09:00.240","Text":"In this video, we learned about electron configurations of the elements."}],"ID":20946},{"Watched":false,"Name":"Periodic Table and Electron Configurations","Duration":"5m 15s","ChapterTopicVideoID":20172,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/20172.jpeg","UploadDate":"2019-08-15T02:39:29.2000000","DurationForVideoObject":"PT5M15S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:01.960","Text":"In the previous videos,"},{"Start":"00:01.960 ","End":"00:05.305","Text":"we talked about the electron configurations of the elements."},{"Start":"00:05.305 ","End":"00:07.480","Text":"In this video, we\u0027ll show how the structure of"},{"Start":"00:07.480 ","End":"00:11.350","Text":"the periodic table is related to these configurations."},{"Start":"00:11.350 ","End":"00:16.584","Text":"Let\u0027s begin with what we learned about the periodic table in previous videos."},{"Start":"00:16.584 ","End":"00:20.170","Text":"We learned that the modern periodic table is arranged according to"},{"Start":"00:20.170 ","End":"00:24.595","Text":"the atomic number beginning with z=1, and continuing upwards."},{"Start":"00:24.595 ","End":"00:30.340","Text":"We learned that there are 7 rows called periods and 18 columns called groups."},{"Start":"00:30.340 ","End":"00:33.120","Text":"Here are our 7 rows,"},{"Start":"00:33.120 ","End":"00:35.375","Text":"1, 2, 3 down to 7,"},{"Start":"00:35.375 ","End":"00:37.105","Text":"and these are called periods,"},{"Start":"00:37.105 ","End":"00:42.970","Text":"and we have 1-18 columns and these are called groups."},{"Start":"00:42.970 ","End":"00:48.610","Text":"We also learned that there are various historical names to some of the groups,"},{"Start":"00:48.610 ","End":"00:50.635","Text":"and we\u0027ll go over these just now."},{"Start":"00:50.635 ","End":"00:57.620","Text":"For example, group 1 apart from hydrogen are called alkali metals."},{"Start":"01:02.870 ","End":"01:07.910","Text":"Group 2 are called rare earth metals."},{"Start":"01:12.790 ","End":"01:19.580","Text":"Group 3-12 are called transition metals, or transition elements."},{"Start":"01:25.310 ","End":"01:30.040","Text":"Group 17 are called halogens."},{"Start":"01:32.720 ","End":"01:41.180","Text":"Group 18 are called rare gases or noble gases."},{"Start":"01:45.920 ","End":"01:47.940","Text":"Now groups 1,"},{"Start":"01:47.940 ","End":"01:51.975","Text":"2 and 13-18 that\u0027s this first block,"},{"Start":"01:51.975 ","End":"01:58.165","Text":"and the final block here are often called main group elements."},{"Start":"01:58.165 ","End":"02:01.870","Text":"The transition from one side of the main group to"},{"Start":"02:01.870 ","End":"02:05.680","Text":"the other side of the main group are the transition metals."},{"Start":"02:05.680 ","End":"02:08.570","Text":"These are called main group."},{"Start":"02:09.980 ","End":"02:14.380","Text":"This also part of the main group."},{"Start":"02:15.980 ","End":"02:20.850","Text":"Then we have 2 rows at the bottom,"},{"Start":"02:20.850 ","End":"02:23.425","Text":"1 row is called the lanthanides,"},{"Start":"02:23.425 ","End":"02:27.549","Text":"and they should really be in the 6th period."},{"Start":"02:27.549 ","End":"02:29.650","Text":"But there\u0027s no room for them,"},{"Start":"02:29.650 ","End":"02:31.000","Text":"so we write them down below,"},{"Start":"02:31.000 ","End":"02:33.006","Text":"so this should really be up here."},{"Start":"02:33.006 ","End":"02:37.765","Text":"The actinides should really be in the 7th period here."},{"Start":"02:37.765 ","End":"02:40.000","Text":"But again, there\u0027s no room for them."},{"Start":"02:40.000 ","End":"02:41.650","Text":"Now before we go on,"},{"Start":"02:41.650 ","End":"02:46.270","Text":"we need to define what\u0027s the valence shell, and valence electrons."},{"Start":"02:46.270 ","End":"02:49.340","Text":"The valence shell is the outermost shell,"},{"Start":"02:49.340 ","End":"02:52.780","Text":"and the electrons in it are called valence electrons."},{"Start":"02:52.780 ","End":"02:58.500","Text":"These are the electrons that participate in chemical bonding."},{"Start":"03:03.430 ","End":"03:09.444","Text":"Now we\u0027re going to talk about the electron configurations of the various groups."},{"Start":"03:09.444 ","End":"03:12.500","Text":"Here, n is going to be the valence shell,"},{"Start":"03:12.500 ","End":"03:15.320","Text":"and also the period is the same number."},{"Start":"03:15.320 ","End":"03:18.470","Text":"We learned already that group 1,"},{"Start":"03:18.470 ","End":"03:20.615","Text":"which are alkali metals,"},{"Start":"03:20.615 ","End":"03:24.560","Text":"1 electron is in the outermost s orbital,"},{"Start":"03:24.560 ","End":"03:26.765","Text":"we\u0027re calling that ns orbital."},{"Start":"03:26.765 ","End":"03:28.310","Text":"Whereas in group 2,"},{"Start":"03:28.310 ","End":"03:30.290","Text":"which we call the rare earth metals,"},{"Start":"03:30.290 ","End":"03:34.870","Text":"there are 2 electrons in the outermost s orbital,"},{"Start":"03:34.870 ","End":"03:37.280","Text":"the valence s orbitals."},{"Start":"03:37.280 ","End":"03:41.105","Text":"Here we have this part of the periodic table."},{"Start":"03:41.105 ","End":"03:45.845","Text":"We were filling in s orbitals and that\u0027s called the s block."},{"Start":"03:45.845 ","End":"03:54.005","Text":"Of course, helium is also part of that because we\u0027re filling in the 1s orbital."},{"Start":"03:54.005 ","End":"03:57.230","Text":"This is also part of the s block."},{"Start":"03:57.230 ","End":"03:59.977","Text":"This part of the periodic table,"},{"Start":"03:59.977 ","End":"04:02.780","Text":"we\u0027re filling in the p orbitals."},{"Start":"04:02.780 ","End":"04:06.440","Text":"There are 6 columns like that, 1, 2,"},{"Start":"04:06.440 ","End":"04:08.225","Text":"3, 4, 5, 6,"},{"Start":"04:08.225 ","End":"04:11.240","Text":"and that\u0027s called the p block."},{"Start":"04:11.240 ","End":"04:16.549","Text":"Here we\u0027re filling in is from group 13 to group 18,"},{"Start":"04:16.549 ","End":"04:19.775","Text":"and we\u0027re filling in the p orbitals."},{"Start":"04:19.775 ","End":"04:21.530","Text":"Then in the central part,"},{"Start":"04:21.530 ","End":"04:23.720","Text":"which we call the transition elements,"},{"Start":"04:23.720 ","End":"04:26.770","Text":"we\u0027re filling in the d orbitals."},{"Start":"04:26.770 ","End":"04:29.600","Text":"If n is the valence shell,"},{"Start":"04:29.600 ","End":"04:36.145","Text":"then what we\u0027re filling is in is the n-1 d orbitals."},{"Start":"04:36.145 ","End":"04:39.000","Text":"If we have the 4th period,"},{"Start":"04:39.000 ","End":"04:42.375","Text":"we\u0027re filling in 3d orbitals."},{"Start":"04:42.375 ","End":"04:46.205","Text":"In the 5th period we are filling in the 4d orbitals and so on."},{"Start":"04:46.205 ","End":"04:49.980","Text":"This part is called the d block."},{"Start":"04:50.710 ","End":"04:54.095","Text":"Now the lanthanides and actinides,"},{"Start":"04:54.095 ","End":"05:01.730","Text":"there were filling in f orbitals, n-2 f orbitals."},{"Start":"05:01.730 ","End":"05:04.135","Text":"Here we\u0027re filling in 4f,"},{"Start":"05:04.135 ","End":"05:06.705","Text":"and here we\u0027re filling in 5f."},{"Start":"05:06.705 ","End":"05:09.140","Text":"In this video, we talked about"},{"Start":"05:09.140 ","End":"05:14.220","Text":"the electron configuration of the elements in the periodic table."}],"ID":20947},{"Watched":false,"Name":"Exercise 1","Duration":"6m 22s","ChapterTopicVideoID":23055,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/23055.jpeg","UploadDate":"2020-12-20T04:26:47.8300000","DurationForVideoObject":"PT6M22S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.410 ","End":"00:03.645","Text":"We\u0027re going to solve the following exercise."},{"Start":"00:03.645 ","End":"00:06.180","Text":"Write the electron configurations of nitrogen,"},{"Start":"00:06.180 ","End":"00:08.700","Text":"germanium, tungsten, and lead."},{"Start":"00:08.700 ","End":"00:11.710","Text":"Let\u0027s begin with nitrogen."},{"Start":"00:13.460 ","End":"00:18.330","Text":"We\u0027re going to start with the electron configuration of nitrogen."},{"Start":"00:18.330 ","End":"00:20.550","Text":"If we look at the periodic table of elements,"},{"Start":"00:20.550 ","End":"00:24.465","Text":"we can see that nitrogen has an atomic number of 7."},{"Start":"00:24.465 ","End":"00:27.300","Text":"The atomic number for nitrogen equals 7,"},{"Start":"00:27.300 ","End":"00:31.875","Text":"meaning that we have to fill in 7 electrons in the electron configuration."},{"Start":"00:31.875 ","End":"00:34.200","Text":"Now the way we do this is we begin with"},{"Start":"00:34.200 ","End":"00:38.390","Text":"the 1st period and we go on until we get to nitrogen."},{"Start":"00:38.390 ","End":"00:39.650","Text":"We\u0027re going to start with the 1st period."},{"Start":"00:39.650 ","End":"00:41.930","Text":"In the 1st period, we have the 1s orbital and we can"},{"Start":"00:41.930 ","End":"00:47.009","Text":"see that the 1s orbital fills completely."},{"Start":"00:47.840 ","End":"00:51.105","Text":"Now, in the s orbitals we have place for 2 electrons."},{"Start":"00:51.105 ","End":"00:53.285","Text":"We have 2 electrons in the 1s orbital."},{"Start":"00:53.285 ","End":"00:56.705","Text":"Next, we go into the second period."},{"Start":"00:56.705 ","End":"01:01.305","Text":"In the 2nd period we have the 2s orbital,"},{"Start":"01:01.305 ","End":"01:03.795","Text":"which again fills completely."},{"Start":"01:03.795 ","End":"01:06.495","Text":"We have 2 electrons in there."},{"Start":"01:06.495 ","End":"01:09.480","Text":"Next, we\u0027re going into the 2p orbitals."},{"Start":"01:09.480 ","End":"01:11.520","Text":"You can see that nitrogen is here."},{"Start":"01:11.520 ","End":"01:13.725","Text":"If we count, we have 1,2,3,"},{"Start":"01:13.725 ","End":"01:18.940","Text":"meaning that 3 electrons go into the 2p orbitals."},{"Start":"01:19.700 ","End":"01:24.850","Text":"We reach nitrogen, so this is our electron configuration for nitrogen."},{"Start":"01:24.850 ","End":"01:32.530","Text":"The electron configuration is 1s^2 2s^2 2p^3."},{"Start":"01:32.530 ","End":"01:36.340","Text":"Now we\u0027re going on to the electron configuration of germanium."},{"Start":"01:36.340 ","End":"01:42.620","Text":"If we look at germanium, we can see that the atomic number is 32."},{"Start":"01:48.180 ","End":"01:53.060","Text":"We have to fill in 32 electrons in the orbitals."},{"Start":"01:53.160 ","End":"01:57.100","Text":"Now instead of beginning with the 1st period with the 1s"},{"Start":"01:57.100 ","End":"02:00.157","Text":"orbital and filling in all of the orbitals,"},{"Start":"02:00.157 ","End":"02:06.110","Text":"what we do in this case is we go to the period before the germanium,"},{"Start":"02:06.110 ","End":"02:08.300","Text":"meaning the germanium is in the 4th period."},{"Start":"02:08.300 ","End":"02:13.860","Text":"We\u0027re going to go into the 3rd period and take the noble gas, which is argon."},{"Start":"02:16.090 ","End":"02:20.165","Text":"Argon has an atomic number of 18."},{"Start":"02:20.165 ","End":"02:24.290","Text":"We\u0027re going to begin with the electron configuration with the noble gas core,"},{"Start":"02:24.290 ","End":"02:26.825","Text":"meaning the electron configuration of argon."},{"Start":"02:26.825 ","End":"02:30.425","Text":"Then we\u0027re going to go on. After you have the electron configuration of argon,"},{"Start":"02:30.425 ","End":"02:33.200","Text":"we can continue to the 4th period,"},{"Start":"02:33.200 ","End":"02:36.575","Text":"and fill in electrons until we get to germanium."},{"Start":"02:36.575 ","End":"02:42.660","Text":"We can see that first we fill in the 4s orbital and again we fill 2 electrons."},{"Start":"02:43.670 ","End":"02:48.430","Text":"Then we go on here we have the 3d orbitals."},{"Start":"02:49.300 ","End":"02:52.580","Text":"Since we didn\u0027t reach the germanium yet,"},{"Start":"02:52.580 ","End":"02:55.130","Text":"the 3d orbitals are completely full,"},{"Start":"02:55.130 ","End":"02:57.780","Text":"meaning they have 10 electrons."},{"Start":"02:57.940 ","End":"03:03.715","Text":"Then what we\u0027re left with is the 4p orbitals."},{"Start":"03:03.715 ","End":"03:07.320","Text":"Here we can see that we have 2 more electrons to fill in,"},{"Start":"03:07.320 ","End":"03:08.700","Text":"so in the 4p orbitals,"},{"Start":"03:08.700 ","End":"03:11.130","Text":"we fill in 2 more electrons."},{"Start":"03:11.130 ","End":"03:15.755","Text":"The electron configuration of germanium is the argon noble gas core,"},{"Start":"03:15.755 ","End":"03:19.760","Text":"and then we have 4s^2 3d^10 4p^2."},{"Start":"03:19.760 ","End":"03:25.030","Text":"Next, we\u0027re going to see the electron configuration of the tungsten atom."},{"Start":"03:25.030 ","End":"03:28.225","Text":"We\u0027re going to start with tungsten now."},{"Start":"03:28.225 ","End":"03:32.090","Text":"We can see the tungsten has atomic number 74,"},{"Start":"03:32.090 ","End":"03:34.490","Text":"it\u0027s in the 6th period."},{"Start":"03:34.490 ","End":"03:36.920","Text":"Atomic number is 74,"},{"Start":"03:36.920 ","End":"03:40.535","Text":"meaning we have to fill in a total of 74 electrons."},{"Start":"03:40.535 ","End":"03:44.630","Text":"Again, we\u0027re going to start with a 5th period noble gas, xenon."},{"Start":"03:44.630 ","End":"03:47.480","Text":"We\u0027re going to have the noble gas core."},{"Start":"03:47.480 ","End":"03:50.135","Text":"Then we\u0027re going to add the rest of the electrons."},{"Start":"03:50.135 ","End":"03:55.835","Text":"We\u0027re going to go into the 6th period and first we have to fill in the 6s orbital."},{"Start":"03:55.835 ","End":"03:58.535","Text":"Again, it\u0027s going to fill in with 2 electrons,"},{"Start":"03:58.535 ","End":"04:02.595","Text":"since we haven\u0027t reached tungsten yet."},{"Start":"04:02.595 ","End":"04:06.070","Text":"After we fill in the 6s orbital,"},{"Start":"04:06.070 ","End":"04:08.300","Text":"we\u0027re going to go into the lanthanides,"},{"Start":"04:08.300 ","End":"04:10.979","Text":"which is the 4f orbitals."},{"Start":"04:12.140 ","End":"04:14.280","Text":"This fills in completely,"},{"Start":"04:14.280 ","End":"04:16.650","Text":"the 4f orbitals fill in completely so we\u0027re going to have"},{"Start":"04:16.650 ","End":"04:19.800","Text":"14 electrons since we haven\u0027t reached the tungsten yet."},{"Start":"04:19.800 ","End":"04:27.218","Text":"Now, we\u0027re going to go into the 5d orbitals."},{"Start":"04:27.218 ","End":"04:33.080","Text":"We can see in this case fill until we have 4 electrons."},{"Start":"04:33.080 ","End":"04:37.495","Text":"The electron configuration of tungsten is xenon,"},{"Start":"04:37.495 ","End":"04:44.270","Text":"6s^2, 4f^14, and 5d^4."},{"Start":"04:44.270 ","End":"04:47.480","Text":"That\u0027s the electron configuration of tungsten."},{"Start":"04:47.480 ","End":"04:50.330","Text":"Now we\u0027re going to write the electron configuration of"},{"Start":"04:50.330 ","End":"04:53.450","Text":"lead and if we look at our periodic table,"},{"Start":"04:53.450 ","End":"04:59.135","Text":"we can see that lead is in the sixth period and the atomic number for lead is 82."},{"Start":"04:59.135 ","End":"05:06.290","Text":"We have lead. Then lead,"},{"Start":"05:06.290 ","End":"05:08.540","Text":"we have to fill in 82 electrons."},{"Start":"05:08.540 ","End":"05:12.035","Text":"Again, we start with a noble gas in the 5th period,"},{"Start":"05:12.035 ","End":"05:14.700","Text":"which is xenon again."},{"Start":"05:16.240 ","End":"05:20.170","Text":"Xenon has the atomic number 54."},{"Start":"05:20.170 ","End":"05:23.895","Text":"We start with xenon and then we go on."},{"Start":"05:23.895 ","End":"05:27.140","Text":"We have, again, the 6s orbital fills in completely,"},{"Start":"05:27.140 ","End":"05:29.034","Text":"so it has 2 electrons."},{"Start":"05:29.034 ","End":"05:32.140","Text":"Then, again we go into the lanthanides,"},{"Start":"05:32.140 ","End":"05:35.640","Text":"which are the 4th orbitals and these fill-in completely,"},{"Start":"05:35.640 ","End":"05:39.750","Text":"meaning we have 14 electrons in the 4f orbitals."},{"Start":"05:39.750 ","End":"05:44.385","Text":"Then we go into the 5d orbitals."},{"Start":"05:44.385 ","End":"05:49.670","Text":"Now the 5d, in this case fill-in completely because we haven\u0027t reached lead yet."},{"Start":"05:49.670 ","End":"05:51.500","Text":"The 5d fill-in completely,"},{"Start":"05:51.500 ","End":"05:53.980","Text":"meaning they have 10 electrons."},{"Start":"05:53.980 ","End":"05:59.775","Text":"Then what we\u0027re left with is 2 more electrons in the 6p orbitals."},{"Start":"05:59.775 ","End":"06:05.220","Text":"It\u0027s left with 6p^2,"},{"Start":"06:05.220 ","End":"06:06.940","Text":"then we reach the lead."},{"Start":"06:06.940 ","End":"06:11.030","Text":"The electron configuration for lead is xenon noble core."},{"Start":"06:11.030 ","End":"06:13.175","Text":"Then we have 6s^2,"},{"Start":"06:13.175 ","End":"06:17.120","Text":"4f^14, 5d^10, and 6p^2."},{"Start":"06:17.120 ","End":"06:19.670","Text":"That\u0027s our electron configuration for lead."},{"Start":"06:19.670 ","End":"06:22.200","Text":"Thank you very much for watching."}],"ID":23879},{"Watched":false,"Name":"Exercise 2","Duration":"9m 40s","ChapterTopicVideoID":23056,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/23056.jpeg","UploadDate":"2020-12-20T04:27:32.1300000","DurationForVideoObject":"PT9M40S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.340","Text":"Hi. We\u0027re going to solve the following exercise."},{"Start":"00:02.340 ","End":"00:04.590","Text":"Show the electron configurations of oxygen,"},{"Start":"00:04.590 ","End":"00:09.090","Text":"silicon, selenium, and bismuth using orbital diagrams."},{"Start":"00:09.090 ","End":"00:11.800","Text":"We\u0027re going to start with oxygen."},{"Start":"00:12.170 ","End":"00:14.400","Text":"If we take a look at oxygen,"},{"Start":"00:14.400 ","End":"00:18.010","Text":"we can see that the atomic number for oxygen is 8,"},{"Start":"00:21.620 ","End":"00:25.155","Text":"meaning we have to fill in 8 electrons."},{"Start":"00:25.155 ","End":"00:29.130","Text":"We begin with the electron configuration of oxygen."},{"Start":"00:29.130 ","End":"00:33.630","Text":"We\u0027re going to start with the first period with a 1s orbital and we\u0027re going to fill it"},{"Start":"00:33.630 ","End":"00:38.595","Text":"in with 2 electrons,"},{"Start":"00:38.595 ","End":"00:42.320","Text":"then we\u0027re going on to the second period we have the 2s orbital,"},{"Start":"00:42.320 ","End":"00:46.475","Text":"which fills in also this time with 2 electrons because it\u0027s full."},{"Start":"00:46.475 ","End":"00:51.505","Text":"Then we go on. We have in a 2p orbitals, we have 1,2,3,4."},{"Start":"00:51.505 ","End":"00:53.010","Text":"The 2p orbitals,"},{"Start":"00:53.010 ","End":"00:55.300","Text":"we have 4 electrons."},{"Start":"00:55.630 ","End":"00:59.755","Text":"That\u0027s the electron configuration for oxygen,"},{"Start":"00:59.755 ","End":"01:03.980","Text":"and we want to write this using an orbital diagram."},{"Start":"01:03.980 ","End":"01:08.720","Text":"An orbital diagram, we\u0027re going to start with the 1s orbital."},{"Start":"01:08.720 ","End":"01:14.010","Text":"We\u0027re just going to draw a square for this 1s orbital."},{"Start":"01:14.600 ","End":"01:18.800","Text":"Now we know that in the 1s orbital we have 2 electrons,"},{"Start":"01:18.800 ","End":"01:21.410","Text":"so we\u0027re going to draw 2 electrons.."},{"Start":"01:23.000 ","End":"01:29.825","Text":"The fact that the arrows are pointing opposite directions,"},{"Start":"01:29.825 ","End":"01:33.985","Text":"shows that the electrons have opposite spins."},{"Start":"01:33.985 ","End":"01:37.405","Text":"Since remember the Pauli exclusion principle,"},{"Start":"01:37.405 ","End":"01:42.140","Text":"that no 2 electrons can have the same 4 quantum numbers."},{"Start":"01:42.770 ","End":"01:47.470","Text":"For this reason, if 2 electrons occupy the same orbital,"},{"Start":"01:47.470 ","End":"01:52.870","Text":"the spins must be opposing spins. That\u0027s the 1s orbital."},{"Start":"01:52.870 ","End":"01:55.835","Text":"The next we\u0027re going to fill in the 2s orbital in the same way,"},{"Start":"01:55.835 ","End":"01:58.575","Text":"2 electrons with opposite spins,"},{"Start":"01:58.575 ","End":"02:01.874","Text":"and then we\u0027re going to go into the 2p orbitals."},{"Start":"02:01.874 ","End":"02:06.880","Text":"Now remember that in 2p we have 3 orbitals."},{"Start":"02:09.650 ","End":"02:12.990","Text":"We\u0027re going to write 3 orbitals."},{"Start":"02:12.990 ","End":"02:15.240","Text":"Now we have to fill in these orbitals,"},{"Start":"02:15.240 ","End":"02:18.320","Text":"and we have 4 electrons to fill them in."},{"Start":"02:18.320 ","End":"02:23.320","Text":"Now remember Hund\u0027s rule that states that if we have degenerate orbitals,"},{"Start":"02:23.320 ","End":"02:25.510","Text":"meaning orbitals of identical energy,"},{"Start":"02:25.510 ","End":"02:31.860","Text":"we have to fill in the electrons initially singly,"},{"Start":"02:31.860 ","End":"02:36.405","Text":"meaning that we\u0027re going to put 1 electron in the first orbital,"},{"Start":"02:36.405 ","End":"02:39.480","Text":"1 electron in the second, and then the third,"},{"Start":"02:39.480 ","End":"02:44.125","Text":"and only now we can put electrons with opposing spins in the same orbital."},{"Start":"02:44.125 ","End":"02:46.120","Text":"Since we filled in 3 electrons,"},{"Start":"02:46.120 ","End":"02:47.435","Text":"we have 1 left,"},{"Start":"02:47.435 ","End":"02:50.870","Text":"so 1 is going to go in 1 of the orbitals,"},{"Start":"02:50.870 ","End":"02:57.510","Text":"meaning that we have 1 of the orbitals with 2 electrons and the other is with 1 electron."},{"Start":"02:57.700 ","End":"03:03.635","Text":"Orbital diagram for oxygen is 1s^2,"},{"Start":"03:03.635 ","End":"03:06.785","Text":"2s^2, 2p^4, and this is how it looks."},{"Start":"03:06.785 ","End":"03:10.070","Text":"Now we\u0027re going on to the silicon orbital diagram."},{"Start":"03:10.070 ","End":"03:13.080","Text":"We\u0027re going to start with a silicon."},{"Start":"03:14.950 ","End":"03:21.240","Text":"We can see that silicon is in the third period and the atomic number is 14."},{"Start":"03:23.650 ","End":"03:28.320","Text":"For silicon, we\u0027re going to start with a neon noble core."},{"Start":"03:30.920 ","End":"03:34.480","Text":"Then we\u0027re going to add, we\u0027re going to go on to the next period,"},{"Start":"03:34.480 ","End":"03:38.210","Text":"which is period 3, so we\u0027re going to have 3 S2."},{"Start":"03:39.150 ","End":"03:41.860","Text":"Again because we\u0027ve passed the 3s orbital,"},{"Start":"03:41.860 ","End":"03:44.380","Text":"and we didn\u0027t get to the silicon yet."},{"Start":"03:44.380 ","End":"03:46.360","Text":"Then we\u0027re going to go on to 3p,"},{"Start":"03:46.360 ","End":"03:48.880","Text":"which is the next orbital which fills,"},{"Start":"03:48.880 ","End":"03:55.150","Text":"and we\u0027re going to have 2 electrons until we get to silicon."},{"Start":"03:55.150 ","End":"03:59.545","Text":"Now we\u0027re going to draw an orbital diagram for this electron configuration."},{"Start":"03:59.545 ","End":"04:03.690","Text":"Again, we start with the neon noble core."},{"Start":"04:03.690 ","End":"04:06.880","Text":"Then we have 3s, just like we did before"},{"Start":"04:06.880 ","End":"04:09.970","Text":"in the s orbital we have 2 electrons because it\u0027s completely filled"},{"Start":"04:09.970 ","End":"04:16.845","Text":"and they have to have opposing spins because of the Pauli exclusion principle,"},{"Start":"04:16.845 ","End":"04:20.290","Text":"and then we have 3p orbitals."},{"Start":"04:21.850 ","End":"04:26.945","Text":"We\u0027re going to divide this into 3 since we have 3 orbitals."},{"Start":"04:26.945 ","End":"04:29.540","Text":"Since these are degenerate orbitals,"},{"Start":"04:29.540 ","End":"04:30.860","Text":"meaning having the same energy,"},{"Start":"04:30.860 ","End":"04:34.909","Text":"we are going to fill in 2 electrons in separate orbitals."},{"Start":"04:34.909 ","End":"04:39.270","Text":"This is the orbital diagram for silicon."},{"Start":"04:42.800 ","End":"04:46.535","Text":"Now we\u0027re going to start with Selenium."},{"Start":"04:46.535 ","End":"04:53.850","Text":"You can see that selenium is in the fourth period and it has atomic number 34."},{"Start":"04:57.320 ","End":"05:00.650","Text":"Again, Selenium is in the fourth period,"},{"Start":"05:00.650 ","End":"05:03.140","Text":"meaning we\u0027re going to start the electron configuration with"},{"Start":"05:03.140 ","End":"05:07.650","Text":"the third period noble gas argon core,"},{"Start":"05:09.500 ","End":"05:12.180","Text":"and then we\u0027re going to add to the argon."},{"Start":"05:12.180 ","End":"05:18.160","Text":"We have to add the 4s orbital electrons,"},{"Start":"05:18.160 ","End":"05:22.085","Text":"which is 2 electrons because it\u0027s full."},{"Start":"05:22.085 ","End":"05:24.545","Text":"Then we go on to the 3d orbitals,"},{"Start":"05:24.545 ","End":"05:28.790","Text":"and we have 10 electrons since we didn\u0027t reach the selenium yet."},{"Start":"05:28.790 ","End":"05:30.035","Text":"We have 3d,"},{"Start":"05:30.035 ","End":"05:32.060","Text":"these are 10 electrons,"},{"Start":"05:32.060 ","End":"05:36.475","Text":"and then we reached the 4p orbitals."},{"Start":"05:36.475 ","End":"05:39.325","Text":"In fourth, we have 1,2,3,4,"},{"Start":"05:39.325 ","End":"05:41.055","Text":"we have 4 electrons."},{"Start":"05:41.055 ","End":"05:42.900","Text":"That\u0027s the 4p,"},{"Start":"05:42.900 ","End":"05:44.780","Text":"and we have 4 electrons."},{"Start":"05:44.780 ","End":"05:47.495","Text":"Now we\u0027re going to draw the orbital diagrams for this."},{"Start":"05:47.495 ","End":"05:51.380","Text":"We have the argon noble gas core,"},{"Start":"05:51.380 ","End":"05:55.400","Text":"and then we have again 4s orbitals,"},{"Start":"05:55.400 ","End":"05:58.640","Text":"we fill in 2 electrons with opposing spins."},{"Start":"05:58.640 ","End":"06:03.120","Text":"Next we have the 3d orbitals."},{"Start":"06:03.120 ","End":"06:04.200","Text":"We\u0027re just going to put in,"},{"Start":"06:04.200 ","End":"06:06.170","Text":"in 3d we have 5 orbitals,"},{"Start":"06:06.170 ","End":"06:09.480","Text":"so we\u0027re going to divide this into 5,1,2,3,4,5."},{"Start":"06:12.080 ","End":"06:16.780","Text":"We\u0027re going to fill in 10, so we have 1,2,3,4,5,"},{"Start":"06:17.510 ","End":"06:21.550","Text":"then we fill in the other 5,6,7,8,9,10,"},{"Start":"06:22.690 ","End":"06:25.535","Text":"of course, with opposing spins."},{"Start":"06:25.535 ","End":"06:28.225","Text":"Then we get to the 4p orbital,"},{"Start":"06:28.225 ","End":"06:35.500","Text":"which here we divide it into 3 orbitals,"},{"Start":"06:36.080 ","End":"06:38.475","Text":"and we fill in 4 electrons."},{"Start":"06:38.475 ","End":"06:40.610","Text":"Again, we fill them in singly in the beginning,"},{"Start":"06:40.610 ","End":"06:45.900","Text":"1,2,3, and the fourth is going to go into the first orbital."},{"Start":"06:45.900 ","End":"06:48.380","Text":"1 of the other orbitals."},{"Start":"06:48.380 ","End":"06:52.160","Text":"This is the electron configuration using an orbital diagram for"},{"Start":"06:52.160 ","End":"07:01.350","Text":"selenium Now we\u0027re going"},{"Start":"07:01.350 ","End":"07:03.400","Text":"on to the bismuth."},{"Start":"07:03.510 ","End":"07:07.190","Text":"We\u0027re going to go on to the Bismuth."},{"Start":"07:07.890 ","End":"07:14.570","Text":"If we look, we can see the bismuth is in the sixth period we have the atomic number 83."},{"Start":"07:16.710 ","End":"07:20.860","Text":"We\u0027re going to start with the noble gas core from the fifth period,"},{"Start":"07:20.860 ","End":"07:25.975","Text":"which is xenon, and build from there."},{"Start":"07:25.975 ","End":"07:30.040","Text":"First of all, we\u0027re going to add the 6s orbital,"},{"Start":"07:30.040 ","End":"07:34.040","Text":"and we\u0027re going to fill in 2 electrons there because it\u0027s completely full."},{"Start":"07:34.730 ","End":"07:37.975","Text":"Then we\u0027re going to get to the 4f orbitals."},{"Start":"07:37.975 ","End":"07:40.060","Text":"We\u0027re going to fill in the 4f orbitals again,"},{"Start":"07:40.060 ","End":"07:44.760","Text":"they fill in completely since we haven\u0027t reached the bismuth yet,"},{"Start":"07:44.760 ","End":"07:47.310","Text":"so there are 14 electrons there."},{"Start":"07:47.310 ","End":"07:50.030","Text":"Next we\u0027re going to reach the 5d orbitals,"},{"Start":"07:50.030 ","End":"07:52.570","Text":"which also fill in completely."},{"Start":"07:52.570 ","End":"07:55.950","Text":"They fill in with 10 electrons,"},{"Start":"07:55.950 ","End":"08:00.600","Text":"and what we\u0027re left with is the 6p orbitals."},{"Start":"08:00.600 ","End":"08:03.905","Text":"We can see that here we have to fill in 1,2,3,"},{"Start":"08:03.905 ","End":"08:07.320","Text":"electrons, so 6p^3."},{"Start":"08:07.840 ","End":"08:11.390","Text":"Now we only have to write the orbital diagrams."},{"Start":"08:11.390 ","End":"08:14.375","Text":"We have xenon noble core again."},{"Start":"08:14.375 ","End":"08:17.500","Text":"Then we have the 6s orbital,"},{"Start":"08:17.500 ","End":"08:21.480","Text":"which fills in with 2 electrons with opposing spins."},{"Start":"08:21.480 ","End":"08:23.490","Text":"We have the 4f orbitals,"},{"Start":"08:23.490 ","End":"08:25.380","Text":"which are 7 orbitals,"},{"Start":"08:25.380 ","End":"08:29.835","Text":"we\u0027re going to just divide this into 7."},{"Start":"08:29.835 ","End":"08:37.365","Text":"It\u0027s 1,2,3,4,5,6,7, and these fill incompletely."},{"Start":"08:37.365 ","End":"08:40.510","Text":"They fill in 1,2,3,4,5,6,7,"},{"Start":"08:42.170 ","End":"08:47.800","Text":"and then another 7 electrons with opposing spins, 1,2,3,4,5,6,7."},{"Start":"08:50.990 ","End":"08:55.420","Text":"Next we have the 5d orbitals,"},{"Start":"08:55.540 ","End":"08:58.535","Text":"in the 5d orbitals."},{"Start":"08:58.535 ","End":"09:00.470","Text":"We have 5 orbitals,"},{"Start":"09:00.470 ","End":"09:05.360","Text":"so it\u0027s 1,2,3,4,5 and we fill in 10 electrons,"},{"Start":"09:05.360 ","End":"09:14.800","Text":"meaning we fill in 1,2,3,4,5,6,7,8,9,10."},{"Start":"09:14.800 ","End":"09:17.835","Text":"Then we\u0027re left with the 6p orbitals,"},{"Start":"09:17.835 ","End":"09:20.980","Text":"we divide into 3."},{"Start":"09:21.650 ","End":"09:25.590","Text":"This time we fill in 3, meaning 1,2,3."},{"Start":"09:26.770 ","End":"09:31.020","Text":"This is our electron configuration from bismuth."},{"Start":"09:36.400 ","End":"09:39.960","Text":"Thank you very much for watching."}],"ID":23880},{"Watched":false,"Name":"Exercise 3 - part a","Duration":"3m 50s","ChapterTopicVideoID":23057,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/23057.jpeg","UploadDate":"2020-12-20T04:27:47.9970000","DurationForVideoObject":"PT3M50S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.260 ","End":"00:03.314","Text":"Hi, We\u0027re going to solve the following exercise."},{"Start":"00:03.314 ","End":"00:06.780","Text":"Use the basic rules for electron configurations to indicate a,"},{"Start":"00:06.780 ","End":"00:12.070","Text":"the number of 3d electrons in a copper atom. Let\u0027s begin with a."},{"Start":"00:13.610 ","End":"00:17.250","Text":"In order to find the number of 3d electrons in a copper atom,"},{"Start":"00:17.250 ","End":"00:20.470","Text":"we\u0027re going write the electron configuration of copper."},{"Start":"00:21.560 ","End":"00:25.025","Text":"We can see that copper is in the fourth period."},{"Start":"00:25.025 ","End":"00:28.650","Text":"The atomic number of copper is 29,"},{"Start":"00:32.860 ","End":"00:36.470","Text":"meaning that we have to fill in 29 electrons,"},{"Start":"00:36.470 ","End":"00:38.180","Text":"so the electron configuration."},{"Start":"00:38.180 ","End":"00:40.730","Text":"Now, again, we\u0027re going to start with the electron configuration with"},{"Start":"00:40.730 ","End":"00:43.850","Text":"the noble gas core from the third period,"},{"Start":"00:43.850 ","End":"00:45.960","Text":"so that\u0027s the argon."},{"Start":"00:47.050 ","End":"00:49.355","Text":"Then we\u0027re going to add to the argon."},{"Start":"00:49.355 ","End":"00:51.620","Text":"If we\u0027re using the general way to fill in the orbitals,"},{"Start":"00:51.620 ","End":"00:55.440","Text":"the next orbitals, which fill the 4s orbital,"},{"Start":"00:56.170 ","End":"01:00.620","Text":"which we\u0027re supposed to fill in 2 electrons and then we have the 3d orbitals,"},{"Start":"01:00.620 ","End":"01:02.615","Text":"which we can see fill in with 1,"},{"Start":"01:02.615 ","End":"01:03.770","Text":"2, 3,"},{"Start":"01:03.770 ","End":"01:05.390","Text":"4, 5, 6,"},{"Start":"01:05.390 ","End":"01:08.430","Text":"7, 8, 9 electrons."},{"Start":"01:10.150 ","End":"01:18.125","Text":"What we did now, is we filled in the electrons in the orbitals in the general order,"},{"Start":"01:18.125 ","End":"01:21.215","Text":"which most electrons fill."},{"Start":"01:21.215 ","End":"01:23.780","Text":"However, of course there are exceptions,"},{"Start":"01:23.780 ","End":"01:26.020","Text":"in this case, an exceptions to this order,"},{"Start":"01:26.020 ","End":"01:27.860","Text":"so in the case of copper,"},{"Start":"01:27.860 ","End":"01:34.310","Text":"we can see that we have 2 electrons in the 4s and 9 electrons in the 3d orbitals."},{"Start":"01:34.310 ","End":"01:36.050","Text":"However, this is not the actual case."},{"Start":"01:36.050 ","End":"01:44.670","Text":"The actual case in copper is that 1 of the 4s electrons actually is in the 3d orbitals,"},{"Start":"01:44.670 ","End":"01:47.899","Text":"meaning that in the 3d orbitals we have 10 electrons."},{"Start":"01:47.899 ","End":"01:51.170","Text":"In the 4s orbital we have only 1 electron."},{"Start":"01:51.170 ","End":"01:58.800","Text":"Again, this is an exception to the regular order that we fill in the electrons."},{"Start":"01:59.080 ","End":"02:02.105","Text":"We can see that"},{"Start":"02:02.105 ","End":"02:07.610","Text":"the electron configuration for the copper as the argon and then 4s^1, 3d^10."},{"Start":"02:07.610 ","End":"02:12.890","Text":"Now what we needed to find in a is the number of 3d electrons in a copper atom,"},{"Start":"02:12.890 ","End":"02:16.790","Text":"so as we can see, we have 10 3d electrons."},{"Start":"02:16.790 ","End":"02:18.740","Text":"As we can see in copper,"},{"Start":"02:18.740 ","End":"02:23.700","Text":"we have 10 3d electrons,"},{"Start":"02:25.850 ","End":"02:31.660","Text":"so our answer for a is 10 3d electrons."},{"Start":"02:32.290 ","End":"02:35.580","Text":"Now, we\u0027re going to go on to b."},{"Start":"02:36.010 ","End":"02:39.650","Text":"Now we\u0027re going to take a look at b and b we have to find"},{"Start":"02:39.650 ","End":"02:43.590","Text":"the number of forests electrons in a scandium atom,"},{"Start":"02:43.910 ","End":"02:49.560","Text":"so the number of 4s electrons in a scandium atoms,"},{"Start":"02:49.560 ","End":"02:52.790","Text":"so we\u0027re going to start with electron configuration of scandium."},{"Start":"02:52.790 ","End":"02:56.195","Text":"Scandium is with atomic number 21,"},{"Start":"02:56.195 ","End":"02:57.530","Text":"and it\u0027s in the fourth period,"},{"Start":"02:57.530 ","End":"03:00.085","Text":"so we\u0027re going to write the electron configuration."},{"Start":"03:00.085 ","End":"03:02.340","Text":"Again, z=21."},{"Start":"03:02.340 ","End":"03:05.480","Text":"It\u0027s in the fourth period, so we\u0027re going to begin with the argon core again,"},{"Start":"03:05.480 ","End":"03:07.620","Text":"the argon noble core."},{"Start":"03:10.490 ","End":"03:14.780","Text":"Then we\u0027re going to add, if you can see first to the 4s orbital,"},{"Start":"03:14.780 ","End":"03:16.970","Text":"which we\u0027re going to add 2 electrons since we"},{"Start":"03:16.970 ","End":"03:19.534","Text":"haven\u0027t rescan him yet and now we read so scandium,"},{"Start":"03:19.534 ","End":"03:24.530","Text":"we have 3d orbitals and we only have 1 electron in the 3d."},{"Start":"03:24.530 ","End":"03:28.610","Text":"That\u0027s the electron configuration for scandium and we were asked"},{"Start":"03:28.610 ","End":"03:33.110","Text":"to find the number of 4s electrons in scandium."},{"Start":"03:33.110 ","End":"03:40.495","Text":"As you can see, the number of 4s electrons in scandium is 2 electrons,"},{"Start":"03:40.495 ","End":"03:44.000","Text":"since the 4s orbital is completely full,"},{"Start":"03:44.000 ","End":"03:47.490","Text":"so our answer for b is 2 electrons."},{"Start":"03:47.720 ","End":"03:51.280","Text":"Now, we\u0027re going to go on to c."}],"ID":23881},{"Watched":false,"Name":"Exercise 3 - part b","Duration":"4m 17s","ChapterTopicVideoID":23054,"CourseChapterTopicPlaylistID":154571,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/23054.jpeg","UploadDate":"2020-12-20T04:26:26.2670000","DurationForVideoObject":"PT4M17S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:07.000","Text":"Okay, so in c we have to find the number of 3p electrons in a sulfur atom."},{"Start":"00:08.390 ","End":"00:11.100","Text":"If we look at the periodic table of elements,"},{"Start":"00:11.100 ","End":"00:16.450","Text":"sulfur is in the third period and with atomic number 16."},{"Start":"00:17.920 ","End":"00:23.620","Text":"The electron configuration of sulfur begins with a neon noble core,"},{"Start":"00:23.620 ","End":"00:28.710","Text":"because the neon is a noble gas in the second period."},{"Start":"00:30.430 ","End":"00:34.310","Text":"Then we\u0027re going to add to the electron configuration of neon."},{"Start":"00:34.310 ","End":"00:38.800","Text":"We have 3s2 because that\u0027s the next orbital which fills in 3s."},{"Start":"00:38.800 ","End":"00:41.190","Text":"We have 2 electrons filling in."},{"Start":"00:41.190 ","End":"00:45.855","Text":"Then we reach the 3p orbitals."},{"Start":"00:45.855 ","End":"00:49.329","Text":"We have 1, 2, 3,"},{"Start":"00:49.329 ","End":"00:52.785","Text":"4 electrons, which fill in there."},{"Start":"00:52.785 ","End":"00:56.940","Text":"In c, the question was the number of 3p electrons in a sulfur atom."},{"Start":"00:56.940 ","End":"01:01.740","Text":"So the number of 3p electrons we have is 4 electrons."},{"Start":"01:01.740 ","End":"01:06.690","Text":"The answer for c is 4 electrons."},{"Start":"01:06.690 ","End":"01:10.910","Text":"Now we\u0027re going to go on to d. In d,"},{"Start":"01:10.910 ","End":"01:15.065","Text":"we\u0027re looking for the number of unpaired electrons in a chlorine atom."},{"Start":"01:15.065 ","End":"01:18.080","Text":"As you can see from the periodic table of elements,"},{"Start":"01:18.080 ","End":"01:20.990","Text":"chlorine is with atomic number of 17,"},{"Start":"01:20.990 ","End":"01:23.915","Text":"and it\u0027s in the third period."},{"Start":"01:23.915 ","End":"01:26.360","Text":"We\u0027re going to write the electron configuration again."},{"Start":"01:26.360 ","End":"01:28.650","Text":"We\u0027re going to begin with neon."},{"Start":"01:29.930 ","End":"01:34.980","Text":"We\u0027re going to continue to the 3s orbital and that\u0027s going to be completely full,"},{"Start":"01:34.980 ","End":"01:36.630","Text":"so it\u0027s going to be 3s2,"},{"Start":"01:36.630 ","End":"01:40.390","Text":"and then we\u0027re going to go on to the 3p orbital."},{"Start":"01:40.910 ","End":"01:43.674","Text":"In this case, we have 1, 2,"},{"Start":"01:43.674 ","End":"01:46.479","Text":"3, 4, 5 electrons."},{"Start":"01:47.110 ","End":"01:50.960","Text":"Now in order to know how many unpaired electrons we have,"},{"Start":"01:50.960 ","End":"01:54.675","Text":"which was what we need to find in d,"},{"Start":"01:54.675 ","End":"01:57.555","Text":"we\u0027ll write the orbital diagram."},{"Start":"01:57.555 ","End":"02:00.240","Text":"Again, we begin with the neon core,"},{"Start":"02:00.240 ","End":"02:02.980","Text":"then we add the 3s orbital,"},{"Start":"02:02.980 ","End":"02:05.360","Text":"which is completely full,"},{"Start":"02:05.360 ","End":"02:08.135","Text":"and again, the electrons are with opposing spins."},{"Start":"02:08.135 ","End":"02:13.180","Text":"Then we have 3p orbitals, which are 3."},{"Start":"02:13.180 ","End":"02:15.290","Text":"We have to fill in 5 electrons,"},{"Start":"02:15.290 ","End":"02:17.820","Text":"so we fill in them in 1, 2, 3, 4, 5."},{"Start":"02:20.810 ","End":"02:24.175","Text":"Again, according to Hund\u0027s rule,"},{"Start":"02:24.175 ","End":"02:27.350","Text":"that degenerate orbitals, meaning orbitals of"},{"Start":"02:27.350 ","End":"02:30.545","Text":"the same energy need to fill in singly in the beginning."},{"Start":"02:30.545 ","End":"02:34.205","Text":"And only then we add paired electrons."},{"Start":"02:34.205 ","End":"02:37.670","Text":"Now if we look at our orbital diagram,"},{"Start":"02:37.670 ","End":"02:42.260","Text":"we can see that we have only 1 unpaired electron in chlorine."},{"Start":"02:42.260 ","End":"02:46.260","Text":"We\u0027re going to write this 1 unpaired electron."},{"Start":"02:47.870 ","End":"02:50.040","Text":"And that is our answer for d,"},{"Start":"02:50.040 ","End":"02:53.020","Text":"1 unpaired electron in chlorine."},{"Start":"02:53.090 ","End":"02:55.500","Text":"Now we\u0027re going to go on to e. In e,"},{"Start":"02:55.500 ","End":"02:59.630","Text":"we need to find the number of 4f electrons in a lead atom."},{"Start":"02:59.630 ","End":"03:03.780","Text":"We\u0027re going to write the electron configuration for lead."},{"Start":"03:03.950 ","End":"03:07.400","Text":"In lead, we can see is with atomic number 82,"},{"Start":"03:07.400 ","End":"03:09.660","Text":"it\u0027s in the sixth period."},{"Start":"03:11.080 ","End":"03:14.300","Text":"It begins with a xenon noble gas core."},{"Start":"03:14.300 ","End":"03:16.505","Text":"So let\u0027s write xenon."},{"Start":"03:16.505 ","End":"03:18.515","Text":"Then we add first,"},{"Start":"03:18.515 ","End":"03:21.245","Text":"we have the 6s orbitals."},{"Start":"03:21.245 ","End":"03:23.450","Text":"First we have the 6s orbital,"},{"Start":"03:23.450 ","End":"03:26.150","Text":"which fills in completely with 2 electrons."},{"Start":"03:26.150 ","End":"03:28.700","Text":"Then we go into the Lanthanides,"},{"Start":"03:28.700 ","End":"03:31.370","Text":"which is the 4f orbitals,"},{"Start":"03:31.370 ","End":"03:37.380","Text":"and they fill in completely with 14 electrons since we haven\u0027t reached the lead yet."},{"Start":"03:37.380 ","End":"03:40.160","Text":"Then we go into the 5d orbitals,"},{"Start":"03:40.160 ","End":"03:43.255","Text":"which also fill in completely with 10 electrons."},{"Start":"03:43.255 ","End":"03:46.800","Text":"Then we reach the 6s orbitals, which we only have 1,"},{"Start":"03:46.800 ","End":"03:51.365","Text":"2 electrons in the 6p orbitals which have 2 electrons."},{"Start":"03:51.365 ","End":"03:53.765","Text":"In the question in e,"},{"Start":"03:53.765 ","End":"03:57.590","Text":"what\u0027s the number of 4f electrons in a lead atom."},{"Start":"03:57.590 ","End":"03:59.450","Text":"So as we can see in the 4f,"},{"Start":"03:59.450 ","End":"04:00.905","Text":"we have 14 electrons."},{"Start":"04:00.905 ","End":"04:07.260","Text":"The answer is 14 electrons since the 4f orbitals are completely full."},{"Start":"04:09.790 ","End":"04:13.580","Text":"The answer for e is 14 electrons."},{"Start":"04:13.580 ","End":"04:16.860","Text":"Thank you very much for watching."}],"ID":23878}],"Thumbnail":null,"ID":154571}]

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